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</style></head><body><div class = "content"><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">Example 1.1: 2D compressible irrotational flow over a thin profile</span></h1><div class = "S3"><img class="imageNode" width="351" height="124" style="vertical-align: baseline" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA7QAAAFOCAIAAAA5M8avAABUoklEQVR4Ae2de5wU1Zm/ewC5rEP4
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TkSuQmCC"></div><div class = "S4"><span class = "S2">The leading order correction of the velocity field due to the presence of the profile </span><span style="vertical-align:-7px"><img 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width="75.5" height="29" /></span><span class = "S2"> is governed by</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="189" height="38" /></span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="129.5" height="38" /></span></div><div class = "S4"><span class = "S2">where </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="22.5" height="20" /></span><span class = "S2"> is the Mach number.</span></div><h2 class = "S5"><span class = "S2"></span></h2><h2 class = "S5"><span class = "S2">a) Determine the type of the system (3)</span></h2><div class = "S4"><span class = "S2">Let us re-write the system using matrices:</span></div><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="179" height="46" /></span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">M</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">assume(M,</span><span class = "S10">'real'</span><span class = "S11">); assumeAlso(M&gt;0);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">A = [ 1-M^2,  0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">          0,  1  ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">B = [     0,  1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">         -1,  0  ];     </span></div></div></div><div class = "S12"><span class = "S2">The characteristics can be computed by</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">dx dy</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S11">determinant = simplify( det( A'*dy - B'*dx ) )</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="7E9E8ABD" data-testid="output_0" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><span class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">determinant =&nbsp;</span><span class="MathEquation Windows inlineSymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,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" width="130" height="20" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">Dx</span><span class = "S11"> = simplify( solve( determinant, dx ) )</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="B9811363" data-testid="output_1" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">Dx =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,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" width="165.5" height="46" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S12"><span class = "S2">Therefore, </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="43.5" height="18" /></span><span class = "S2"> would lead to two real characteristics and the system would thus be hyperbolic. On the other hand, no real characteristics can be found for </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="43.5" height="18" /></span><span class = "S2"> and the flow would than be elliptic. The critical case </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="43.5" height="18" /></span><span class = "S2"> is parabolic. This result is confirmed by experimental observation that supersonic flows contain shock waves, while subsonic flows are smooth.</span></div><h2 class = "S5"><span class = "S2"></span></h2><h2 class = "S5"><span class = "S2">b) Convert (3) into a second-order PDE using velocity potential</span></h2><div class = "S4"><span class = "S2">Substituting the velocity potential </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="168" height="20" /></span><span class = "S2">, the equation (3b) is identically satisfied</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="110" height="40" /></span></div><div class = "S4"><span class = "S2">such that only equation (3a) remains to be solved. After substitution:</span></div><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="200" height="42" /></span></div><div class = "S4"><span class = "S2">We can classify second-order PDEs based on the coefficients multiplying the highest derivatives. The generic form of second order PDE reads</span></div><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="240" height="47" /></span><span class = "S2"> </span></div><div class = "S4"><span class = "S2">where in our case </span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">a = [ 1-M^2,  0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">          0,  1  ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">b</span><span class = "S11"> = [     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">          0      ];      </span></div></div></div><div class = "S12"><span class = "S2">The eigenvalues of </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">a</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S11">eig(a)</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="9C4DA6B5" data-testid="output_2" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">ans =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,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" width="69" height="42" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S12"><span class = "S2">have opposite sign if </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="43.5" height="18" /></span><span class = "S2"> and (4) turns into a wave equation. On the other hand, the eigenvalues have the same sign if </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFcAAAAkCAYAAAD8fqYDAAAEUklEQVRoQ+3ZaahvUxgG8N9FxswRPhiKTBmKQsYUPpgiIWMiZB5SJHOGyDxkCpnnMn1A5pkoKREfKENR5ilzT73/7P6dc///e8/e556rvep8OGev/e61nvWs533e98zSj84QmNVZ5D6wHtwOSdCD24PbIQIdhu6Z24PbIQIdhu6Z24PbIQIdhh7F3DNw7tD3z0F+/hmxrt1xB5ZszNsRT3e4ny5DB6t1cCpexQ2jPjYK3IVwAG5tBErQE/HrbIKvhJuxc815F0fgzTEOZdSa58XzFXAyjiqyBJO7Ri1kFLh5f0u8jI+wFp7Agfh2kuCJeRyuaDw/r9j+16gFzbDnS+BwHI/VGmtrDdwdcC2uxIV4A/vh60mAWBf34Jk6mM0QiXh0hgE3u+UsgO1xAT6r/S+Dq7Fy3eZWmBsJ2A1h32W1on3w4QSrWwTnF8Mfxm14D3vjg/kI3MjhSXgHz+JvrI37sFFb4C5ejB2Adj02QRLT6xOAldO+pTR5/TqQB3EYvp9GcJfCLohW5sa1MVoHd5US7tdKQ2/HTgXucNZftjLod6Wv0dy9SkriOrrW22j9GqX3yQnL4cw64BkJ7uZ4CsfgAVxeWX9Y0LOxsPP0AjQA31ssH0v8p7D7xbBdZfKwNeOl0sfHR7iaOfls68w9CNcUU98qFpw2ASNWx53lJC6uRPYCvsSueHtOdjHm3BVLy5PNN8A35atjAd8vnRwz1FjTWgV3YVyEZPu4g08RYJNB4xoGVz3in6Jii7Jon5fmJvk9j/3xxVjLHz0pWXy9uj0Hl+dMwrwR9+Or0SHmekar4EZDU2GFffF5vxRQYWizkNgUdxebIwWL4tK6pteV+f5trrf034uxePnu1vWn2L1YxFjDP1uIPypEq+BuiGT6VGdhasagoHiygP6jtC3PjsUPGCTB6GDsTHS6jTH4diQmcVPYxCJN12gV3HjbR4YKgAHgKSAiFZGC9B4OwSu1y1i1x8psb4sXW9r9/4a5yf7J/DH/zQJgzXIB0ePU2tHg2LSzGlczBUbkIQzbFx+3BG7CRHM3LpnaY37V3HSyomfxis0+wvLle+N10xlKZyxW65MCcMGGo4heH40fWwS3GWpVJKkdWnX/fOMW0qRIkoqdahYA8ZQDr5uNBvjU2IP249LVDUvxMG5rcqrYpxoLi3OTYskyZrTP3aaAPXKob9lkZoqKtBGb3bE5Fv2pItt4P5YwGn9Clb55NOMqtOhtmjWxUxNVV9HZOIPo6XCy2hMP1Ya3aiS5FjEcGWrQ1M7BJ/GmkdTGaCbq3JLc4Nn+w2C4n5vfc7ViylM8JFFdMmYJGQ28qtxFNpPG8k3T5EEnAy+J9/cpIBsZTPMqTahTGjciHcGz8Rx+xk8TfWMY3IGXbM4dpxAYuIicbnM0K7kp7HGevNqUuFELmFB+xvlPxKjA/fNJEOjB7ZAaPbg9uB0i0GHonrk9uB0i0GHonrkdgvsvEMr7JTDW0A0AAAAASUVORK5CYII=" width="43.5" height="18" /></span><span class = "S2"> and (4) can be transformed to Poisson equation by stretching coordinates. The type of the problem is therefore conserved.</span></div><div class = "S4"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h2 class = "S14"><span class = "S2">Example 1.2 a): Find the characteristics if they exist</span></h2><div class = "S4"><span class = "S2">We know by now that characteristics exist for </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="43.5" height="18" /></span><span class = "S2">. The characteristics of a 2nd order PDE with 2 independent variables can be computed by solving</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="222.5" height="44" /></span><span class = "S2"> </span></div><div class = "S4"><span class = "S2">for </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="40" height="20" /></span><span class = "S2">. In our case</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="154.5" height="44" /></span></div><div class = "S3"><span style="vertical-align:-24px"><img 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DHY/ijxBHAJiZpUC5CNezj9LATtXpRnZYxfj+MyZ0gAlSbKQV2F0eTMl/uuui8lyXlw35pUC5BNajhH0ZkykHlMGiBiwUgznwXIRjF08RHrIgHOMKiCeO27uoiNj4gO4s8ICMajBSdyb6jFMJfsfqEurstIx3cOJgFPnIO5gXAd2EiyaUGyEINI+BP1q1EN8b306wmjWdZVbLDO1nlxqIt1pBTXNJUA9jjYTNIiQPvj7Ex+EKLAsSlB5JBuAdbxImMaCQjNc3s2fe8orw+QjXJY4qOmJIEA2ZRGM/oySgkEyEY5LPFRU5JAgGxKoxl9GaUEAmSjHJb4qClJIEA2pdGMvoxSAgGyUQ5LfNSUJPB/0EJiioa41WoAAAAASUVORK5CYII=" 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src="data:image/png;base64,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" width="124" height="28" /></span></div><div class = "S3"><span style="vertical-align:-8px"><img src="data:image/png;base64,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" width="125.5" height="28" /></span></div><div class = "S4"><span class = "S2">where </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="23" height="18" /></span><span class = "S2"> const. and </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="24.5" height="18" /></span><span class = "S2">const. defines the characteristics. We can then find the solution </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="52" height="20" /></span><span class = "S2"> as a function of </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="43" height="20" /></span><span class = "S2"> and </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFkAAAAoCAYAAACVdVbLAAAGXElEQVRoQ+2aZaguVRSGn2snKhYqoqIXFbHFLhQLMbG7u0WwuxOLayJ2oNhgi6Jid6JYIIKBqIgdPLC2bMbJc74z1wPfwPlxvtmz99rvXutd71ozExheY47AhDFfYbgAQ5B7cIIhyEOQe0CghyWGnjwEuQcEeliib0+eHlgDeBr4pYf9DXqJ+YH5gBeAv9tO3ifIcwLHA1cA77U18H82bgpgB2Bq4Ebgjzb29QXy3MDJwCXjGOCEp5htB0zXFug+QJYizgGeB27tEmZtvGQyjXFPZwAPAE802dAHyJ762sCRwE9NBo2j+4uG8xwGfFpn91iDPA9wNXBuJLtxhGGjqWJ3ODArcArwZ9UTYw3ynsBawIHAj41mj78BSwGTgH2AdyYHyLMA1wCPAVeOP/xaWTwzcDnwOnBRVb4p82R/WwU4FVgxQv084FdgKmBT4ABgXeDxkGUmteK1PHBXZOKy+2m8892bPbwTcHP8PwNwMbBXdn+/ARzaLsD12ZyrA89m/6scVEPuUyA/AzYPMIv7PAZYLmz8vuxoykBeGdgDeAk4DvgmgPoyMuqGwFfAMmGAnqrR3s+vfeN3daVG1kXTksBVwEoBoFz3czywQEglixiLAAF/u5Wf1a/pPm6PPeQHm54Sm5Piz3W3Bz4pmVInOR3YBni/Lch6jyQ+U3iUJynn7A+8BtwE/AZsBdwR4G4CvJItMCVwGjCx7oQLBm0Znm+hsnXGcQuF9HP4IABOy84b+1P57ArcUALQCRHRx0ZElyU3I/b+mOPRtiCncYsFiO8CH8Up3QL8FQPS/TmAIsgpzDUq98o6B5wrlIieIZjXBj0p/bYAdh9wIZNyhs5yYjhFbl/iW5PbtsAHFcYr5YyICysOqrZpvx7wSEx8ZoRNXkauBjwTHqwW9iDSNXt4yauA3lApbwqGq0ZMlpashwbY6wCHAB+OkiKKj8u7FwTvmrSOjghN48xH9wCX1nixYxcBbou8YvT+56qTcBK64JoQ5Kyi4PZ0nfzOEkpIIPts6cIVgC0YdKRXvwVMG/KvjtNHg32iA9VPHnEmeLWv8rNs7/majXutAjnP6hpiCZl3nRLnehAa419+v3HhCmSSwNfDPDz1tUl2rK4d41AfBHYGvouFVoj1TfxJ6VTZ0LjXKpDzpLA+UCT0nM+kCjmp7HS70oVKQt25cU0EDRLwRIkPAwL+LTBjaF7X0bubWgGJk8XgrC50oYyTjz+uIP00sR5v4nizMPlIEt8SUT2ZqRcGlIApAQ4S2HyupAyMlpTcdBrVhDRR3FeZHQkLa4lSr6/y5CTWy/jWhZIHqJHVwV8XVu8q4dzsZeHFKhiFv4XM3YDJMIXxoMEuOsvvwHWhbEzAbRrzSQDI376MaJX4mvg2hZGSpSwrp0UMPyumpmLE6tL63zaoXKyCkTYE2yJFrswrwkECnfh0A8DiRPloQ74NTSQ7jICjomDLFda/dpZ58mwhoeTFzYD7KqjAUK4rcdWXqo+9CyVrPl0C2EjII2Ia4OzYrEXCwcAPBTuSMigmrS6HkCf45wAdrIseTw5pt/GgKv4uAzkVGerIMr5NSdEQ36gGQBOIFKAUK2ueJICXBp4EdgM+zxDKdbpZ3jlSqe2wBHKetLoA7Nj8MO0Sdo0aCzE1vbRq8VR6lYGcGjYPxaL2LvIrJUXBa6ICS2UTSBmvGpJSTrqK1JMrHMcUtewgQHbeVA9YjCS6antYNsm0QwepbNyPpJ+ckqIn2NQnlnoS3w6SV/PmTV1eaALLd48enq0C1Uwxgdc9b6HkywibVbVJsivIeXgpc0p1YcEys66ebJk8KJWQ+hwmSLtjI3n7LZ0JkrTXhYfT9taMxG6+qD2criA3JcWykzc5HBE3pIe2fYwqL7LktWkkMHYHS2VTgwsLsE6iArID91STyxfuGwH2uc8HXm56tivIKgZJ3g9TKvunJYv6dtcXjvZlTXJt9GeV7X6/YSL0+43S/m3hwaQgrD6lBvsj9n9Xjb55V3s676UryCkpjkQ2aZyhZRWlIhgN0E3Ok98vJlDvvRH5RNnWxY60hxfD+1s92wVkx+pBdtXk4i4tzLRpv8DRk5Rqrb6+6YJmxdhlo9xdPCLJlw4WPvYpul5KNhPeF10e7AJyl3mHYzMEhiD34A5DkIcg94BAD0sMPbkHkP8BUMGAOAQvO1EAAAAASUVORK5CYII=" width="44.5" height="20" /></span><span class = "S2">, by converting the differentials</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="248.5" height="36" /></span></div><div class = "S4"><span class = "S2">This brings the equation (4) to the normal form</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="60.5" height="38" /></span></div><div class = "S4"><span class = "S2">with solution of the form </span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="139" height="20" /></span></div><div class = "S4"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="32.5" height="20" /></span><span class = "S2"> and </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="30" height="20" /></span><span class = "S2"> can be determined by substituting the Ansatz (9) to boundary conditions. As further simplification, we use educated guess and say that shock waves should not travel upstream of the profile, therefore</span></div><div class = "S3"><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="205.5" height="20" /></span></div><div class = "S3"><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="205" height="20" /></span></div><div class = "S4"><span class = "S2">where </span><span style="vertical-align:-8px"><img src="data:image/png;base64,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" width="89" height="28" /></span><span class = "S2">. </span></div><div class = "S4"><span class = "S2"></span></div><div class = "S4"><span class = "S2">Assume a parabolic profile </span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">x y c epsilon</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">assume(x      ,</span><span class = "S10">'real'</span><span class = "S11">)</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">assume(y      ,</span><span class = "S10">'real'</span><span class = "S11">)</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">assume(c      ,</span><span class = "S10">'real'</span><span class = "S11">); assumeAlso(c      &gt;0)</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">assume(epsilon,</span><span class = "S10">'real'</span><span class = "S11">); assumeAlso(epsilon&gt;0) </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">p   = 1-x^2;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">y_p = epsilon*p;</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S11">p_x = diff(p,x)</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="6F12F1B7" data-testid="output_3" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><span class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">p_x =&nbsp;</span><span class="MathEquation Windows inlineSymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,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" width="29" height="18" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S12"><span class = "S2">The velocity on the profile surface must be tangential to the profile (no penetration boundary condition):</span></div><div class = "S3"><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="199.5" height="22" /></span></div><div class = "S4"><span class = "S2">Subsitution of (10) to (11) gives</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="238.5" height="36" /></span></div><div class = "S4"><span class = "S2">which after integration gives </span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAf4AAABMCAYAAACMGtXvAAAR1ElEQVR4Xu2dCfB+1RjHv5V9zS6Msk3J2jA0sjapSNZI1ppCqVSibEUZSShFiUJCSEo0hiyRMmmkKRMlM2QfW6GEsc1nOmfm/N/ffd/33vvec9fvnfkP//73vfeczznPfc55zrOsJ18mYAImYAImYAKTIbDeZHrqjpqACZiACZiACciK35PABEzABEzABCZEwIp/QoPtrpqACZiACZiAFb/ngAmYgAmYgAlMiIAV/4QG2101ARMwARMwASt+zwETMAETMAETmBABK/4JDba7agImYAImYAJW/J4DJmACJmACUyWADtxY0ksk7SBpS0nXSDpT0jGSfjlGMFb8YxxV98kETMAETKAMga0kXSDpMElHS7pe0taSTpZ0saRXSbq2zIOGdI8V/5BGy201ARMwARNokgCK/0BJuycKfgNJb5e0q6QdJV3S5Av78Cwr/j6MgttgAiZgAibQJwKHSNrLir9PQ+K2mIAJmIAJmEAeAreV9AFJ/K9N/XkY+6kmYAImYAIm0AsCWMF3kfQ2SbtJurAXrWq4ETb1NwzUjzMBEzABExgsgSdJOlbSfpK+PdheLGm4Ff9YR9b9MgETMAETqELgoSGED8e+86v8cGj3WvEPbcTcXhMwARMwgaYJPFjSCcHEP9qdfoRmxd/09PHzTMAETMAEhkTgHsG8/8Exm/fTAbHiH9L0dFtNwARMwASaJHBrSUdJujwk7flfePjNJL1C0l8lfarJF/bhWVb8fRgFt8EETMAETGAVAreQdKSkA8JDLpO0s6Srwt83k3S6pIeFv18taSdJ95R0hqTbz3k5zn6jO++34l9lqvm3JmACJmACfSHALv1FIQYfRU7+/bhbR9c9XdI5obGY9Q+WtL+kwxd04PFjDOmz4u/LlHU7TMAETMAEViVwy2C6f42kUyTtI+mG8NDnSvq8pKj0/7bqy4b6eyv+oY6c220CJmACJlBE4ImSPiPpOknPl3SFJBz4PiTp15IOShYDkyRoxT/JYXenTcAETGC0BGLKXYrs7CnpC5LeL4lz/SOmrvQZdSv+0c59d8wETMAEJkvgWZI+Ien7ktaXdF44ArhxskSSjnet+AmleELwmvyHB8QEShC4lSRMed+RZCEuBma5KjGRfMs6BMYmV3eS9BFJzwlld4+T9G+P+U0EulT8d5P0FkknSvqxB8QEKhAgteZLJb1L0p8r/G4Kt1qupjDKefo4FrlCr20fnPg2lvReSW+W9M882Ib31GWKf0tJ5y6IcSzqMeaVvSUt8pjE0YLqR6zC2lL69JVYzjdI+m5w9BjeiI23xfeVtK+kf0k6VNJ/lnSVFJuc4Y1J+WOS3DzEH+8gaYvA4JrgoHSRpC9LulTSfwv4WK7GKx91ezY1uUKGXhjC9Cit+2pJd0ic/OpyHNXvlil+OkvCA5T5I4KTBAkSZpX6ppKOlvRYSYeFPzED0iwwzJB8rPmIfVrSvPuaBM0u6MAwCWbjO5t8j59VnQCOOK8M1p87B6VPkYwyFwJ+/3B2N3Qz3iZBbl4W5OLDQdnfMdQEpy44c3fewtpyVWbGTOeeKcoVcfwvl7RHyLqHMx9Z+Qjt4/t/TEv6pvezrIziv0tIgrCdpHdKOqRgN8Zz3hr+8DH+7IKe8+9PDgMR4ytzgYqTnxKLmHzilSZ2yPVuP3cxAeJtiat9Y5JNi1+w2y+r+FF2LDi/IunsAQPHZwFFfy9JbwrHX+lChn7y0UL5z1tYW64GPAEabPpU5Qqljwc/Sp5Uu7HQzjPDt+HCkNDn5w2yHuyjyih+PkZkP0JZL1KYLw5nKtuG3XwRlI0knRRWYTnTIGLu2TqEbvxK0vGSNgwhHbTBir+7Kcucw4SNAmM3i0K7VtL7glWpiuKnF48JiwWE/bfddav2mzmy+FiwlnEMxXlkkfUC+fpkMGPOLqwtV7Xxj+aHU5arqPQJ1WMjwLclWpLZ8J0m6XHBsniyd/3lnPseJelLQTx2lHTJHFHhw8R5CikTOZMsunaXRO7jZT4Aq0ojE+G1kn4g6ZvhPJTjCD6YHFlY8a9KuP7v+UDBnzN8smjhcJNalaoqfszfLOxY4ePFO6QLz2OSipBk5NTg40BRkKJrq7BAIL84BUXSy3I1pFHP09apylWq9PkWYJVG8UdHvg2CBRHLInqJY4CoE/KMxLpPTa11vUn/W2bHT6EDsiB9SxLK/Tc1abG7Y7X19Y4c67pW/DiYPEMS/gbH1mTYh58xkbH+PFrSexoKqVtF8cMEEzhHUShArAdDuWgvMoGlAlN9HSvY1OUqx3zsYv7k6McU5CrOfxbE8SKG/4vJ358anNTjf2pz4zdIxZ+ultiZ4NhXN3YaywE7PD5wOPa1fXWh+FlY3S+cOxF+VtV5LTKqW3lqdme4CnPMybsFcxnms1XnQ9qWVT9QRJ+wOH3eAovUKn3P8Vt4ssvfpiCneJX3TVGu4NPEfLRcLZ5pQ5SrKrLTxr25FT9RGzgE4y/FESpWDTbXRDTg44YF9XWSfph2dtmOP11NYTrnPDZe/BYLAH9Qan9cQpFdGQ1cdBSQcyDaVPxx9c7RB7t8LhLOkDaS6lB1Fk91Kk+tWoSCdxKpgdc9iTAwpTGBKHKB38c8s3TVcVxV8cdzPBYjKNM6F6b0Cyr+sOqxRPr46HTEf2PBcmbFd8fbpyRXOeaj5Wr+xBuiXNUUo2w/y6X48WPju/FuSb8PPlLfkHTz4ORI3gKuQkv9MsWfKkuc9r4WHsZLnxbOVvlg4ZRE/PW8K1oOHhTOWP6SDfP8B7eh+O8u6QVBURIGSXIZwq8w5/5oTux1FRRtVZ6KxxJ4yZJZkQXEWcHz/HsZMmCtqvjjApXwnaKokzKM21T86U6TnBJ1F8NTkavc89FyVSwhQ5OrMnLe9j05FD96e5cQ/cPxID5zqV9d6tB4QoigWycz7jLFP3s2UgQN5cBOa9F1m3CujUPXKscFqwxaLsUfk66w8yKGNO6KCc86PazGVmn37G9zVZ5iLjBhsMoQ/sixBJMJhzkWL/z/XDkXVlX8UbhQhLT9700Cz/CsNFJmlSOTMctV2/PRcrV2og9NrjKI6sqPzKH4Hx6ONpF/fBuoR5Be6fe0UD8vU/woacIjqG6UJu5hJfgOSWQXWxS+FxsTG4KX/bIdWa6dVw7FTygWH252xVwkJMLDPMeuOLLMUXkKRcQ448jJ9dWwUMNMVOdYoqq0rKr4yTNOGNwDwtHTn6o2oOX704yYZRbO85o3VrnqYj5artbOsqHJVctivOZ1qY4p25aqC//UOkX4IvlzZsN/444fqzOWeXIYrHMtUvxxN0H4Q1HiHhQ4sfJlPP3jB4oGLEvOMiTFH9tKiCM+EJwRF6VSLTsJyt7XdOWpOGGxVhD2wvFNm5nwVlX8cGM+Mh7Mx74r/hiTT7sJby3y5seCRB2L9OLIJV1oj1WuupqPlqu1X6AhyVXZ72eu+9pQ/A+R9DlJ95mn1CXFjQX+WIXHiIsU/7LEPUwIPArLmFarfKDaGJSmwjm62PHDp+nKU13ssNJxnpriZ3HFah3BxCfkyoJJH/1osCKxIMOKhJMlv4lHLmOVq67mo+XKir9p/dO0qT9uCPDcR6n/oaDB8R58ywr18yLFH1cN10sqStxzu/BC/n3ZVcUkuexZdf89h6mftvCBfmQAnHq+5zrjz1V5qij0cGhn/KyCiTCpE8ufy9JUNF9ZNB8u6bJwvHLVnElNUSn8RDDZFR0JjFmu2p6Plqu1kzAqrb7LFQXfMHnnvJYdi897d5OKP3UKnndEkB5Zkf4ba/2aa1FncPL6eAOJe3jpmJ2QUqhYQHDwIzEL5yxNe/W3VXkKhYLXKDtMlE7fvfqjcDEWdZ1H+6j4cTgjI+GsiT/OuanIVe75aLkqVltDkaupKP50ETEvlDg6qZLnIo3EW2eE5yn+MiuLKqurqYQdRSaEH7H7pyIUipOriTj+titPMdHw4zg4cWDsYxx/3PmSGCrN011ljrZ5b1xUL9vxR5PdvKyZU5OrHPOxi4puOfpRNH9XPUIbmly1KcNl39Xkjn/ZeJIVFksAumfht2We4r9rCOHaPlQLKzQXlO15uK9MLv+Kj6x0ey5T/6JG8FHBeWv/JJFPnaQvXVeeKjrOqOqNuojTsgm9bKAfGMJbSGaxqDLksue09e+x/gWr8nnOfanJbu5ZXXBmXFYjI2e/upCrpuaj5WrxzBiaXOWc53Wf3aTiT58163CPtz96hjmN4v/Zopw58xQ/Fc8I4Wuykl2MPaSK2prwgrpUK/wu/di2XZsZzpzXsoPDGYNQyLJX3ypPxeMMVpdYApoI90sTThwn6aCkyEYZTuSboP4BxW6uKPODju9JBZgwRLJsxaIiNC1N0IFj32zWzLT5U5YrONSdj5ar5UIwNLla3qP272hS8fNd4FtBZBw6dFdJPw2peV8fvsXE9OP4R5bduYn1ihQ/nq0opr0CoyODI9KqH/i4g8FUTKNyJYNJhxbonIMSAgGYmD4XZyrOhc6TdIOkMg6KTU0ZjlEWZTlM39PnylOkhiTkr+44wgGldu9wJIL5mwu/CKwiZ4ezbdICL3pHFAZi+PcJ49nUWOV8DlksyafNORzyQIYtnBI3CfUsWCTCh2vuWV0Qep4zdbmqMh8tVzel2x6jXOWU2T48m+JoZwQfMpyvUfxYZijtfVRwAiYnCyF/bBgoS7/mmlX8KH2ytJGYJ71WrcwXn0UhAULp2qiiViWmso75vY1J0PfKU3UZpKb9Zc9YdqSAVeqUoDhZLAzpYjHMgofESZj8ceK7OFQSQ3BxOMR8xzHZPM9/+mu5qjbqlqvlRbaGLFfVZsOw7kZnPyVsXEkcR35+NueUGsbczyaCTUO8CksB1w1RqIuKhQUFXohNHtpHum6f/bu8BFB6JF7Zt8GiQXlb3PzTLVfNM536Ey1XI54BbSt+ULKzYcdPYoE68dYjHg53rSIBiiJh5uZ8vwu/kYrNzXq75Sor3kk93HI18uHuQvETgsTZAxdnERTu8WUCVQlwTouTJlWncAis62tQ9b19vd9y1deRGVa7LFfDGq9are1C8dNQnO44uyQNKQ52U/9o1xq8Cf8oZlnbPOz4U4/4CWOxXE158Bvou+WqAYhDeERXij8qf85lLw/V4Kz8hzBjum8jc3Y7SdRJwBPeSn/dMWFRbbnqfp4OrQWWq6GN2Art7VLx02wScRC+9IuWq8GtgMw/7ZgAnqvMmatbqoTYcXdrvd5yVQvbpH9kuZrQ8Het+CeE2l01ARMwARMwge4JWPF3PwZugQmYgAmYgAm0RsCKvzXUfpEJmIAJmEDHBGL69D1CIpwtQnsuDYVtjgjHiB03M+/rrfjz8vXTTcAETMAE+kGAFNjkr8f59SxJx4diNs+WRM2Mn4R02aTBHfVlxT/q4XXnTMAETMAEQk0LctlTyRLlj6Kn1ggXBcdOk3Tdoop2Y6JoxT+m0XRfTMAETMAEZgnE5FYo/pMkHTBTzCvWbiBS6JApJJWz4reQmIAJmIAJjJkA1VkperWhJMz6FMKa9GXFP+nhd+dNwARMYNQE0HHs8DHtU8VzSKW7sw2MFX82tH6wCZiACZhAxwTSEsx76qZyxJO/rPgnPwUMwARMwARGS2AzSaeHbJ/bSrpotD2t0DEr/gqwfKsJmIAJmMCgCGwl6YIQo7+zpKsG1fpMjbXizwTWjzUBEzABE+icgBV/wRBY8Xc+L90AEzABEzCBTAS2lHSupN9J2ilUg01fRXEiYvsvkXR+pjb07rFW/L0bEjfIBEzABEygIQIbSTpV0jaSDpVELH8s5U2Vz8MkbSpp76D8G3ptvx9jxd/v8XHrTMAETMAE6hNAx+0i6URJpOzljP+akK2PPP1YA/aTdGX9Vwzvl1b8wxszt9gETMAETKA8gfUlbS3pQEmc+XNdKOmjks6RdGP5R43jTiv+cYyje2ECJmACJmACpQhY8ZfC5JtMwARMwARMYBwErPjHMY7uhQmYgAmYgAmUImDFXwqTbzIBEzABEzCBcRCw4h/HOLoXJmACJmACJlCKgBV/KUy+yQRMwARMwATGQcCKfxzj6F6YgAmYgAmYQCkC/wevHNqJ0kKDpAAAAABJRU5ErkJggg==" width="255" height="38" /></span></div><div class = "S4"><span class = "S2">where </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">a</span><span class = "S2"> remains an undetermined integration constant. Before and after the profile we have a symmetry plane at </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="38.5" height="18" /></span><span class = "S2"> (no-penetration in case of irrotational flow): </span></div><div class = "S3"><span style="vertical-align:-7px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAigAAAAoCAYAAADUkgGsAAAU10lEQVR4Xu2dBfA2NxHGn+LursUGKF6kuEtxdyuuxd2LF3dncHd3h1IYtBSHQQstXtxhftMspPnu7s3lcvLefzPzTfu1994lm2Tz7O6zm93kzSXgEnAJuARcAi4Bl8DCJLDbwvrj3XEJuARcAi4Bl4BLwCUgByi+CFwCLgGXgEvAJeASWJwEHKAsbkq8Qy4Bl4BLwCXgEnAJOEDxNeAScAm4BFwCLgGXwOIk4ABlcVPiHXIJuARcAi4Bl4BLwAGKrwGXgEvAJeAScAm4BBYngZ0EUM4j6Z+Svrm4WfAOuQSOLIFzSjqapK+5YBYjAXTlXpIOkfSTxfTKO7JGCZxe0mklfU7Sf9Y4wNwxDQEop5H0miDIG0g6KPejEz/HGK8r6YySnh1AysRd8M+5BHpJ4JiS7i7pG5Lev2IldSVJH5T0Kkl3k/SHXlKa7mHA4p0k/UbS61c8H9NJ1L/UJYGjSLqZpKOHvYFhvSPbEIByQUnvkvT1IMxfLlCCjO/GkkCkT3dw0nuGOCivKOneku6zYBDae2AT/YD1dw5Jt5d0dUlnl/RtSe8JYPmHHf3gUNxX0rdWDFJYV0+TtF/4s0RrkXm4p6Sf7UBw4vt/uKI4qaSbSsKIv0wAuR+R9HxJn5D075ZPoDtuIulYKwAppTIYVAeFgx9r4nmS7ivpr8PnsvobLhGUPArmsOpvX+8L2RwXCIfGNSR9NQA9DldveRIwcPxcSR+Q9MSwBgEqjwivuMsG8HFySftLevIKQ5Mo3qdKumtQxG/IE+vkT3FIXFLSAyX9afKvz/NB3/915I5B8lJJx5P0cEkHSiJ8+1BJV5b0KElPkvSXls8dW9LjJL1b0kfrdGnytwySQakHhd89MvzBssY7sbSGciek86Itntw5ZLp7OEBB/McPHXCA0n8mAMeEQA8OHpRDwyvYOzcPVhFyxbrq4kVdWtIdA9D+bf9uLPYX7M/XSjqXpGtK+uICe3q2oNvuv0KA2CZu3/91FiLr+4WSLirpFskZBEh5naTzSbpl0BNt3kMOeIyUe0nq8rjW6XXdtwyWQSlAOaGkl0Ruq0/WHVeVt91O0oVDeKINoVb50EpectxwEOJ25+DAO3ZDSQ9xD0rvGUaWz5G0TwAnWFFxO7WkV4bw2WOCp+pfLV/BzY6VBccrfU/vji3oB0sPER81GGDoDuTfNj8LEumgrvj+HyS+XX7M+cMZ+fLAJ4u9b7a28Kp8WNKtJP285fOc0ejkE23QE3V7X+dtg2VQClDOGg4whoEL9Ht1xlPtLXYAoFg+VO2t634RrHE4Dy+IkDqW/qsdoPSe+ItIerukPwYQnxLIUVAAkwdL+njwqMBxaGuQSR+wQZH17uTMP1h6iBjPDt5XwnBLTQCoOYW+/+tJ88TBmCA5487Bk5K+3Qji/HfCPV3n1HkDZwVPKpzPbWhVZFAKUHA7Q/B5c7AQD1+YxK4VUCcHbJfiX0q3TyAJrgcusWcupVPh4HSA0n9CjPwJ94Q1+OuGVxj4I3MFBUV8uq1Zxhwhy7f2787ifrENIWLmEB7WnNlFfJuwHhyE388wi26glAndvIMYyvCXPtPwGkI38K4I8+ClfkLHpwi1w2X7Sgg5LpFMnna/igxyAcopJF0nxIovLukkUW9+FKxA4u2Eev5WNqfVfnWMQEjENd5F3o3DVHycdE7igb8KPTEQZh3LsXT7DALZn0nSPcJ3kSnkSSzrpbSpFJTxEcgYohG75YCIQ3MseNYYG5uGdwwX6d+XIqzQj5j8iYsXgvafG/oIR+XT4b8To2Zsbc3eyd560ALHvGkKSJvcIxCtmWPi8nH7cshsIrRI1tLcCth0w5c2HByxEmY8rEdIjfQ/BmE2Vg4hnskNF/Hso0PmB4YLYUH07VTy8f2/aWU3/3/zDlLH6EZhTadPktnCnr9Ki75Ln8fbuudCHQJNUqgig00ABRYxLqqHhUwEMnYQ+uMD+x7F+t6geNiYeFU4WNhEczWzNt+ZQd5lfPSXvmPJXjVCuyhVMgywWmmgXFIihwIwvnnZ8G68JrRPhe9gKS2JLzOVgkIGxFifFcBam+eBlN03SqLoHuATcnausjZl32ddtlk/Xe/AtUldD7J1moCW/Ra3LR5IiJg5wJR1erUBKf2sO+RFPY/cVoMcTYr/Y4OHkEMWjxypu4AR/glJmD1Flgz/DvAku2fOfWBzcz9J6JGudoawbq/dYOSwFrB8GRc68baSPtZjzZpnFR18qdCJt4V5/OwEZRPWtP9jgyB3/efsy6Z3ASY4I7v2j3lFMIq7PK32fqIC7KM2wJMzpql0IH2pIoMugIJVi6LAc0JaFPFYFIkBACxZY9/znr2DywrSD0pwrroofZQLgoxjZTFh0chJyKAGOMELxeIijsgBS9EnDjKsbApyteXD5yy8sZ6ZUkExBtYNHBjWEIWK0jVkblGeBaH3SXueanPmWkaxizdHEaKgntLCacmZ/zkAysVC7Jz+Ea44IBzOFn+PQ8R4PMkMRLHBt8EYyPU05Iy/zzP07xU9souMc0Q6KbwD6lzEugXLty84ifuLsXT+4I3j/RxuGIroZLJBmkKIfcbb9uya9v+UAMV0TRdAifdjDkAxb92tB/Aqp9KBrKcqMmgDKDC6sWTwIOBS5pC2anYmKA6HmONh2QaELChMNVfGgYVm+li/thFjRjWpYC+ThMUSj7/PxjfXNgcvCytWLHgCftHnZTM8O7WC4hB+R4flYQcbgHGpmRUx8OjyoPQFKKZgKfa0xKy5dHna/jlVWPt4V60ZRycNeRDy5MDFc0AG2VyEQLIqKJ+QC4Ljw8aMHAwOPCfUurhD8C7X2MJTGjq+//vPWLwWagIU0xcAd0J9S27VZNAGUMjMAZ3jjmRzxQepxZaa4utsbCyPOUtXs6mwxPqU34/TPiEs/ljSi0M4AYu+pNQwCpoDylyzKF7cvdyvUPK+tgU5pmU8tYKCm0Dpc7Jf0toYBoA5oHMPjjk28VgAxWRDVkkXX2WOMaffZE0CICnXn4LJmKMDaI+V7XECSRwDpy37YYrxYf1dPiO7Ku7LFYIxQz0XQt/se0AOHCTCMbUb++FywTNloWIscb7Xx7PY1S/f//1nrdrhnHzaMmcx4JbEU2ySUDUZNAGUmDyaekI2se9tQee4rPpPfd4v6AOFlfocYowLz88zQhwZPgQADLBVCibM4kVhoaggRI4RxlkTQIkP99QDRuiO2iyAPrgqudyTvFVT7ynufIJfAZm8pgfFZENV2aUDFPOy/q7BE9JVoC1eyzlhr3qzduQ3AVDYv20ZWE3fJVTMfOP5gWfDgQJAG7sAHV5a9gqWNXLv4zneJL+pAcoa9r8laeAlrOlBsdAxGUFLByjVZNAEUIzDweJNvRAxeGnK3d5WgMJYzb1smTWEYIYcglN5UDYpmSH/f2oFFfM38OJZ+XOsRYjMEEpTj96Q8Y3x2xIOSo63YJsAinGJmjypbSFi5mKbAQr9v56ktwTSO+u0liejaZ02eVAg2UPsrfVd3/9lGqIv/yIn4rBNAAWpVZFBE0Axy78prdbcTCCkJjaxxZbb0isJpVBdjoOfA2eMVhLiIZsAdzNZDvBEKCtcw0rvIrc5B2XX2Y+Z7XHqLe52MsjgRJXeSTEVQSweQ1edIAvZ8DwZIJuyRWxfxsCtz/4Z09OW9sNk3ZRW2xUijg2gNPxj35hCh5SEeCgTwH1LABMydjDuvtBngjKfbeOg4L2pnaI9NUAZc/9PSZI1gE512LZrHOJsP86dTeUDzEDBaOuqmdK1jKbSgfShigy6AEpTmMYIqNzGSnpUfDdIvLjS+3lMqQBgxq730ZckiyVC3JZ4LiEEJh9yXlf54UxdcqTHSEdE6QLQCAN4Fs+uUoxdg+bit/scuK8GblFpyG2qzZlbJdYIv9/N5EuZgi114c8BUNIwTRwibipOZd5bsmFSxT6lDulLkqUKK4fM9yX9I1iPm64w6KND2gwdbsQl3DdWEbepAcqY+39KgJJTJdayYSk5MZUHdSodyNquIoMugELsNC1jb6ioyTICGHDAp3HnMwd+BwifdDgr6DZWHK1PmjFKm5RGqxhJQS2yj0jlu/5IVTvJUOD91PEg3ZjmdVD+r65j63u/4M2imBGA+JA+Wn3GZ83V32VBmbcxtxozhwW1QobUQZhKJDaH6U3nsRGThogBduxF6kek95dMrUP6pBljbEB+hxsAD4TKoFxzANGeLJ4fDBD6TqqDYmJaw/43usBegX/YdJmuhToZd85lmduWxVdFBk0AJc5ooTDU+8LKidFt6n49ZSCI4aruCo9MEUc7WcgiIhuk65ZlUqmx4mDf3ya6rdQOjjcFN9VYN8gSViIjBXkZC39OYmCTHp3agqIP9k0ALWEPskEgMJeGdgacD8U/jTdnU0G5+KDOTcmnPghKKvVcFndyxB9aRgulualn89PwLSMQM/4UaLEXIKXTusIjU+gQc6ezH7tCb3CiuBSSu8gAV1wIF4ephoaKd0ol2XgprmH/xyU3KFOB1zw9R8zYb7pMsGlrEhol+WOJd9819beKDJoASpzRQkoTgjws3BNDdgKoML47BBc8fBJir1g//Ilvbow7X6JcUGZYJihyLGr+wGEhhocCQQlgWXKQ0czFTigpLZdufTFwAkBJwZYhW9zMKEqAzpgNeVMh1YrbjcXNKRmDgTU8ARTs+3zHS0yxNHne+nzbQnSE2QDFeLRK69D0+W7NZ+M9hGUNnya+Kp39g+ckt6ihARrewfqfq4BZrozijJa4jlJTiBhZXShUUqZmCuFhlHobQb1Eh5w7pDPjKY3ryOBtpbot/6SKtK1vk/d3otL16dgNnGDQpWDL9g1lGoZ4/ua+i6fP/o8zcEp5Ush4DfufcbCm2eOcQ6wBzlJrhAQhxuIZRG823dUTrzc701hrZIa1na+5+3Oq5wbLoK0OCqEPLD+sApQoxYaIg0LspLonCpeqsmxq+Bu4IuEHEOLpKgVfolwQpnlFIJ/FoAOLEk9HenhiwXGHBf1MXawxOOHdxP+oeWIpwLF1S80SKr9StXFIRk/uguBAnvNuGdYDc0mtCrxnAD+7+4ZDAxAIZ4JrAdJ+1vK2xPebjO3Fyp2XkudYZ4BN9gcgl3+HR0N9DEA8dz5hWeVkXDAHhEaZD6tSWtKnKX+DtwQPJnfv8E/CIIQ2qSvE3zEudg97FOOG+3gAMwDcrr1WqkPQFXiD0zoyeCkALqmVy9+5rqDJ+jVwAtBkTtEz3NtjLb7GAJ4IlbjH8sTWnNMh+z8GKJvulurq81r2P7LE68G6R19yHsHdBGSw9gHKAFBIr5vOFjv/ADxzFUAtWWeDZdBV6t4se1y0bFQ2cdxQKOR5cxcPhNocolapcrHiToCH+HZRlAfpvCiAGBhZ+XrqEaS3v8Z1KhhPE0/A3G823lJiYsmkzvkbAxk5fUhlUgugWKYYZNg49JbTp6U9Y6mglDkHNGNNUVEVpUSBslxLiHUOD4d1uQ0Hnc0D48ciZm1ABmTvWUNpEwKiPhCKO7eAYakOsXWFMUL4kAaIJFuPME5s4fL/CNNRSRojLfUcWsVjG0vKI4qNHJ6Zsy5Unz0xZP/XAihr2v92huL95wxFRhgkrHfueIu9ql3zhO4ASO/T4zd95n3MZwfJYNNlgdZxngMEQGzddDV012BLlQvvTIsnkW5HYTVS+w5q+Ch8GEhqWEzbpNTHXCxjvtuqCOeSPpv6wjpjzrCw8TzgkdvpDbBNVWcO1rHDjWPK2qxAPBlxiLjvN0t1SNPvAE+WsZMaWBam47LD1ADq2+ed8Lxd5Mk855A+ff/nrQrjchwciodu8rbkvXVLnsoFKLFFkFOzoW34pcqF96FIIEsS3ySdD1RKaey2eiVYR/uHi5VS62hLpmdrumkprFiWuHdLCa1GlMQtvm28k7EmC6uWmilY8nPe8Dt0fBb2IESMV7b0xvNSHWJl9AlNEr4mnMrli4C/tnolkP/hqPDcGDVNhsp0Sb837wuGJEZjSTkA3/+7ziggmvpP+854Ae9s6ywXoFhYBEJsnztu0oGVKhfeQ+ofhxaENJQL5FgUTZd3hFgxpcFhP8Od8FZfAub1QIlDcMyJqTb1wm6+hTBmGRH1e7tdbyR8yRXrrPNcd/BSR2hhkZyqmV1jKNUhRjREh6E7AEldBo71AY8PYWU8enPd0L7UObV+2cWQBwZvU27oMh6X7/9dZ3nHA+RcgGJVL4kTs7FLN2qpcmHqjDyFokDZATyaQjvpNPM76lKA6ol7e6srAbwnWE3EVQ/IIHzxdawCDl7WErVxqDnD3+EzQQT1eTqCr4IsONBx7257I00acnCciVcypiE6BII9XB6Ihhg8lIXfxJ1DR+4taY+QUtyVBFAynjX8BjIowI8wZI58fP9vnnX0KkCaM5dssB0V2jHx5AIU4xfklOTtEj1Im1t9IZ2hLFKk3VUt08hTxDjhwfCe3EnbMxyCeGCo4OptXgmkJGR6A4DkAHNwcgQ4wWtCWj/p1tve4luKh4SIkcMmHdJ10R8HKYcohg2ZQ2Tg5DT0JMCGMBXkxm0OteWMd+xnfP93SxhwQkiHcxJSfe45N/a8Tf7+HIASl+7OKcmbDoIMHEhmgA+qLKJ8abCZiUNTbdI4Il0AxSwn0GQJP4Hfkypd6v2ZfHJW+kFIX6TZsQEpC87cc2hgKYxx2/M2ivF04RDEu7SGZmW9qf9QEiLuo0O6AAr6hXRtah+h+Ps26rQATg7v+0N//n8S8P2/eTFghCOnbamcvXlEhU/kAJTCVxf9DNcfdRK4sjy1HCFQkZFDiIfCcd5cAi4Bl0AsAbvrB85cWtCKys14pWglBo5L2iXgEphYAksCKCgQCjVhVacKBB4JlhFx7Fy37MSi9M+5BFwCM0sADwchGMrPxx4Su62cWk7wekpInDMPzT/vEth5ElgSQOHiPMhoKBdibnASKARHxg5uYVKMHZzsvDXqI3YJ5EqAQlaHhsJoZwnVO+Hx4H0lru/gJFeS/pxLYAESWBJAicVBcSqyF0g9o5ojKawoHm8uAZeASyBHApZ5SHo2BR3hnuRkmOS8259xCbgEJpDAUgHKBEP3T7gEXAIuAZeAS8AlsFQJ/Bd8YD6D5Op6bwAAAABJRU5ErkJggg==" width="276" height="20" /></span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="201" height="20" /></span></div><div class = "S4"><span class = "S2">which leads to</span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="185.5" height="20" /></span></div><div class = "S4"><span class = "S2">where </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">b</span><span class = "S2"> and </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">d</span><span class = "S2"> are integration constants. Due to the hyperbolicity we can assume that the incomming flow in front of the profile is undisturbed, </span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="37.5" height="18" /></span></div><div class = "S4"><span class = "S2">Moreover, we want a continuous velocity potential:</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="217.5" height="36" /></span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="120" height="20" /></span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">phi_0 = x;</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S11">xi = piecewise(y&gt;=0,x-c*y,y&lt;0,x+c*y)</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement" uid="87941D35" data-testid="output_4" data-width="1173" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">xi =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img 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" width="121.5" height="40" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S11">phi_1 = piecewise(xi&lt;=-1,0, xi&gt;-1&amp;xi&lt;1,(xi^2-1)/c, xi&gt;=1,0)</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement scrollableOutput" uid="3FAA2D53" data-testid="output_5" data-width="1173" style="width: 1203px; max-height: 189px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">phi_1 =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img 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" width="419.5" height="137" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">phi = phi_0 + epsilon*phi_1;</span></div></div></div><div class = "S12"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h2 class = "S14"><span class = "S2">b)</span></h2><div class = "S4"><span class = "S2">Let's try to plug in some values</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">c = 2;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">epsilon = 0.1;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11"></span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S11">u = diff(phi,x)</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement scrollableOutput" uid="13F47F00" data-testid="output_6" data-width="1173" style="width: 1203px; max-height: 182px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">u =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img 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" width="452.5" height="129" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S11">v = diff(phi,y)</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsSymbolicElement scrollableOutput" uid="C00EC568" data-testid="output_7" data-width="1173" style="width: 1203px; max-height: 145px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="symbolicElement" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="embeddedOutputsVariableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">v =&nbsp;</div><span class="MathEquation Windows displaySymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img 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" width="425" height="93" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S12"><span class = "S2">and plot the solution</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">xmin=-2; xmax=2; ymin=-2; ymax=2; n=10;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">figure(1); clf; hold </span><span class = "S10">on</span><span class = "S11">; axis([xmin xmax ymin ymax]);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">fplot(subs(H),[-1 1]); fplot(-subs(H),[-1 1]);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">fcontour(subs(phi),[xmin xmax ymin ymax]);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">fcontour(subs(xi),</span><span class = "S10">'k--'</span><span class = "S8">,</span><span class = "S10">'LevelList'</span><span class = "S11">,[-1 1]);</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">[x,y] = meshgrid(linspace(xmin,xmax,n),linspace(ymin,ymax,n));</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">quiver(x,y,subs(u),subs(v));</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">legend(</span><span class = "S10">'upper surface'</span><span class = "S8">,</span><span class = "S10">'lower surface'</span><span class = "S8">,</span><span class = "S10">'velocity potential'</span><span class = "S8">,</span><span class = "S10">'characteristics'</span><span class = "S8">,</span><span class = "S10">'velocity field'</span><span class = "S11">);</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">xlabel(</span><span class = "S10">'x'</span><span class = "S8">); ylabel(</span><span class = "S10">'y'</span><span class = "S11">);</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsFigure" uid="C775B749" data-testid="output_8" style="width: 1203px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="figureElement" style="cursor: default; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><img class="figureImage" 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" style="width: 560px; white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"></div></div></div></div></div><div class = "S12"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">1.3: Time-dependent diffusion</span></h1><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="210.5" height="40" /></span></div><h2 class = "S5"><span class = "S2">a) Classification based on coefficients</span></h2><div class = "S4"><span class = "S2">The generic form of second order PDE reads</span></div><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="290" height="47" /></span></div><div class = "S4"><span class = "S2">Let us select </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="138.5" height="20" /></span><span class = "S2">. Then the matrix </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="15.5" height="20" /></span><span class = "S2"> and the vector </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="13.5" height="20" /></span><span class = "S2"> for our case are given by</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">alpha</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">a = [ -alpha   0      0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0      -alpha  0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0       0      0  ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">b = [  0 </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       1  ];  </span></div></div></div><div class = "S12"><span class = "S2"> The eigenvalues of </span><span style="vertical-align:-7px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAACnElEQVRYR+3WS6hXZRQF8N9NyITMQTpQG4iI2qh84EBFQVRw4EAIM00hCAp8oYIIvhVRxAcOSpQE31iD1HxAooOCIAcO1IGFThooimaolGKEsWUf+Xs8V++Vc++d/L/J/3E+9vr22mut87XowtXShdia4F3CfpP2Ju2dykBTcJ1KdwHWpP1ltL+LT/ARxuMuzmEnbmFDfj/T3tm9jPZ4Nhpf4a38PIp/8yAb0RNX8/elOsGjy324ibm40FC8F75J0FOYjb/qAu+PAxiZhY+XCvfAdnyBYGAl/qsDPOhehK3Yj/m4Xyrc2PmnONRe4NhfNfO+CToRrRUehCPoh6mlkbT5HFXgkxDKvYzp+K2iWrHnLGbidpsRGzZWgQfl2/AjZuHPUuFuWJ1z/hpL8KhhzxysKDkgGIrR/IS1eNIa7SGeddiVs39YAh+Cb/EBvsx9xZY3sQmDSw4YgRO5/4fW4rVRxVXg8Xwz5uEBpuCX16H8VZ2H1cLfARLrjZzv+xiOd/L3H3WCx5wPIop+jPPonsoflsGzB7/jc9xL8AVYjKC+cMDAHEs454U8qBLcgAQfkzl+MS31M5ZhLCJ04lCfpRueCihFOCGFeiP/G4rvsCUt/Iyo1rL9Q6zCtATZge/xGMuxvoHqIgsi/yOYYjU6YBxOYjJ+bRxRne/zPjiM0xm9BU5E8IwSG0+f1Qle2CmAYkSxCjZCBwvxT0d1HkKNgArwawlShEskZgjuuVVX55F6oYP3SvasDJfiBHWBF2+5iOLovkjFqqh9pdrbmxuFncKmkfdr8sYTbEQ2xGXjTkfRXnXY3nkhuZL5EDbtkJlXgY/CsXwPREa8sOqaeblwXMPi4nkdS/F3Z4AXN5y3sRe7M6IrNdRRnbdJsP8D8VqMKQ+LfcYAAAAASUVORK5CYII=" width="15.5" height="20" /></span><span class = "S2"> </span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">eig(a)</span></div></div></div><div class = "S12"><span class = "S2">imply that the matrix is semi-definite, and the </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="79" height="20" /></span><span class = "S2">:</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">rank([a b])</span></div></div></div><div class = "S12"><span class = "S2">equals the number of independent variables. Thus we conclude that the PDE is parabolic.</span></div><div class = "S4"><span class = "S2"></span></div><h2 class = "S5"><span class = "S2">b) Transformation to system of first-order equations</span></h2><div class = "S4"><span class = "S2">The original equation can be transformed into a system of first order equations</span></div><div class = "S3"><span style="vertical-align:-54px"><img src="data:image/png;base64,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" width="216" height="118" /></span></div><div class = "S4"><span class = "S2">by introducing the auxiliary unknowns </span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="102.5" height="36" /></span><span class = "S2"> . In general we cannot say that the system is equivalent to the original equation, because the transformation can create spurious solutions. The solutions of (1) still solve (3), but not vice-versa. Therefore, the type of the first order system can also differ from the original equation. We will see that our example illustrates this problem. Let us write the system (3) in matrix form</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="188" height="48" /></span></div><div class = "S4"><span class = "S2">where </span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="93" height="32" /></span><span class = "S2"> and</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">alpha n_x n_y n_t</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">A = [  1    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0    0     0      ] ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">   </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">B = [  0   -alpha 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       1    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0    0    -1      ] ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">   </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">C = [  0    0    -alpha</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">       0    1     0      ] ;</span></div></div></div><div class = "S12"><span class = "S2">We can analyze the system either with Fourier method, which analyzes whether solutions can have the form of a plane wave, or with the method of characteristics. Both methods lead to similar equations in the end. With the method of characteristics the normals to characteristic surfaces are given by</span></div><div class = "S3"><span style="vertical-align:-7px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWIAAAA+CAYAAAARZxFCAAARWElEQVR4Xu2dBew1RxXFTyluxYsEd3d3dyju7trgxV2KS/Hi7h7cvaTFgwULxQpFgxXNL50Lt8uszMp7u2/vJF++5P92Z2fOzJy5c232UJRAIBAIBAKBrSKwx1a/Hh8PBAKBQCAQUBBxTIJAIBAIBLaMQBDxlgcgPh8IBAKBQBBxzIFAIBAIBLaMQBDxlgcgPh8IBAKBQBBxzIFAIBAIBLaMQBDxlgcgPh8IBAKBQBBxzIFAIBBYAwInlfS61NFbSTp8Tp0OIp7TaERbAoFAYCoE9pJ0oKQTSAoingrlqDcQCAQCgQYEjiPpWZL2lLSvpD/PCa2QiOc0GtGWQCAQmAoBI2Lqv5+kv0z1oT71BhH3QS3eCQQCgaUhcExJT0mN3k/SEXPqQBDxnEYj2hIIBAJTIvDIVPnjp/xIn7qDiPugFu8EAoHAEhEIIl7iqEWbA4FAYKcQQDd8mHNjm03nQiKezVBEQwKBQGBiBHBbo5g/8cSf6159EHF3rOLJQCAQCAQmQSCIeBJYo9JAIBAIBLojEETcHat4MhAIBJaLQIQ4L3fsouWBQCCwIwgEEe/IQEY3AoFAIBCYBIFQTUwCa1QaCAQCgUB3BNZKxKeXdDdJz5hbOrzuQxdPBgKLRIBQ4/tIOljSJyX9e5G9GLnRayTivSU9MZHwt0bGM6oLBAKBdgSOJ4kw43clMm5/Y8efWBsRMwH2l/RuSR/a8bGN7gUCc0bgnJKeLOmhklYvEK2JiI8u6QGSTijp0ZL+MedZGm0LBFaAwM0l7SPpHpJ+u4L+1nZxTUR86SQN30nSd9Y86NH3QGAmCCAUPU/SIZKeu2Z98VqI2Ab8x5IeK+mfG5qIxLZfdo6JqDfU/7E/E3gOR9QSpH96JjkXribpSen6otUKSGshYgb7JZJuKumg4XO5Uw3owF6R/r240xvxUBMCgefw+cF6v4WkR0hCLfC14VUOruHEkl4m6UuSnrpBIWlww8esoA8R31jSy9MlfLQFkpnd1SMOJAx0B6S7qu4l6Y9jApip69iSyHt6d0knqfzOhvDhib+/a9UHnuOM6JnS8f/aleo+kaTRn43zmV61wB83S5vED3vVsPCX+hAxXT6dpFdKuuICiPh8kt4q6YXp8sDSIbuhpLe5l7iAsMtVK/gpI3VwnN7mJC/t7xjPn13SmySdv2NlHEm/nNyZ3iPpT5n31oxnDkaMzxeXBLGyDi/hHvqCpB9JgmQ/IAmVHIUbjJ8v6dAkLGxKRdc2DS4siXF/0EzUJW3trfudMGpOHAirl5f0G0kfTdyDz/S/6l7sS8R2/xM72dwlYhbw0yQhjTJBS4rp06jDyuck3dJN7lx99h43xXYh7ZI2LeFZ5tV5kzoIsrDy2UQMf09/ILDmWpL43z9z32TAsb+tHc/qmF8g+eFeJ/3w9eSSyWmPzY+/Q7qUWztysw3yUen5ucylk0l6TVpTcz5dN+EFtqhYjp82ObgGddrDE/c8JqlespeW9iViGsTx+3ETETHE96LKJOozaWwBQwpt5Jmr/9yS3pIA9b+3qRggltdLenXCp0/bl/4Ocws3Qf5ZyW3ap0lS2vXdc2DOHDCXpsDzf+Agab3KbV5ciImxy1RuR5N0m3RirRLx9SQ9PUlsc9APW69MsGPT7rNOt71WTp7WOacSNr6PuQZBxm9IGyTjQlL6/4smnCMR+wXsd/M+YJ86dfwnkvroh21DqH6bTYjovLrwTFzlAPxGKZSzT9t34R3brJuImN+uWgmw+bmk6zrsAs8jETSDpZ0yCEy6S7r+x88XM4DdwAkzrCukMyTmO0v6/cwmGJIwHk3XlMTJaUkFl9gD0+Z374pqbc8kjLAWPiLptpKY30cpcyRi02OxewwlYtM9oc8GiBKdmE1mjBzoiJH+raB3o32/rpktTCqO3Ozuv1rIjLI0gadMhpMxXIm6EnFOp3wZtyADT+lYafMnKMlK3fow0iWM2J7ZK5HFNxPhzS3HA9I6Ic+3SyfJhSwb+U0PA33OQ8oLGtnT9ByJ+EqSXivpVCMQsQ3uw1I4ZcngIoW9P7mfoftBzWDGp6rE5uvFyk8yIXZC03ddIe2SuOjMtcyJiD2+geeRM6aqJvtq4YZ5FklvTAZrTmsY+5DOIL/DZzApWW+fkYT+enbX3TfgY8IefOWFB/+KFzSyXNRGxFUrIJWjhH6fJCTFO3TQEeNhwYDjfXDBBksikjC7IaI9Da8rdZ3NPY/HAqReKln74wTqBVzOsDYjBVup2/2MONBrcgTEEEFQx0srYdX23D1Thej4zKCIzokj512T0QV9OeSOFXaqsk0itk3PDEycYOyIF3geOeJVNRmeQCUqBiPidyajEesRb55PVSaUPQfBUFjrzPvfScID6f6SUHnglYFumnaMkS7gHJLeLAlj+JIMdrjdscFhMCVO4duZBWpr6+p1fNlExJdLVm8WAi5bHM//Jukikh4sCSmPUuc1Qd0M2DNTI/Fc4FjEzo6u6pJp56NuBpJFiMSJqM/v6MHQGeGC48s3GlQCVQzsaFxKxGYcoj4zHjA56IsVrLx1emeU9oRsniJhRzBJzlqKVELbCPwwf05UA7zLZsBxlM2LgpQwZVTgtogYDOgXkgLli2mD94lg1o6n91Ky+VfqrQTObO5PSOsQK/7Ha+wcrEGCKyB6EvMwPrhiMge/L+mMyViI8MAax0VraDGpkVPjvpLwOOpbqiqxLvWUCHi+PpIWsSE1nVC8uvWDyaX1KKeQOiI2owDSbNUKSCO8JbBuQph19wdpR/2paz07K7vIidIA+13Z7x6lBFpHxKUgm+8wk9B0y/4IwndKj4Z1k8GOZC9IOjwWCgOLZMAmyIJAOiyVgLpMPv/MpokY6z4eE2xmnAqYrO+Q9EBJzJm+ZRfx9AvZcJn6CG9khl8sY4U09xBJv5B01uRuhrCEhIwwNbQYEVM/J9kh6pJNErF9q4kPvBtsZyL2RgEkM6RfJGFffMU5ImZH5e83SRFmVQX2cSU9x+243pC2bSK2SDxUEn63N1/HazggcLnCcj2koLbBHQnyPbNz/rY6baB3gYibcIJYOHHkgjlK8N1FPP2a2AQR2/pEmGLtXjRJqb9MH/ftmSMRl8yXIc96HhydiO1YfqkWC2aTH7FJj3TSuyH5Ttv71R1i20RsRhEkeO9qgqqAoxlHEStdo+zqBtvXyTEPvTM+h96ibTgN/ZZvg0mNJZOwjwRWlUzaAjrw1OAYjB9xH73jruK5aSI2t0/UjzlVkW/PGMII83BMibhkXg95dlIi9ou06UjfRMRmJGvaJeqe2SYRo6pBF4xhDDchyM+Tonlh2OANjdPn5ICumTBVvDK4QuYPbmZ4g16dcbDPRNoWEedOTxgm8clGf0lhQ0J/yYmpxN2Qd3cVz00TMTp5Lk5AJYLBGB9Zvw7MoEdWQ8J5xwgOWSIRe9396BKxESQTuy8Rl+hoqh2Ygoi76pq9T2AXgoM0hjigm6WYyL+cf6FJJpww+oRod+mDPbNpHbFvGwZJclOge6RgqEOthXG3pOwqnrlQ+zFPSFWMTb1TJ2iYX6x5VIyR1H1MY13JnBn6bKmOOGvkzxnrxiRirKlIcm0DBaEdkRAZk4hL3deunAxG7PAEbVhOBBusY0hCR4xEaaUtyq5poE3CrpvwpuLhyD518qBtEnFO4uu6eXp8dxXPnFoMKXWod0Fubnopzxur/bPmQVT3ex9yG9N9rUQQtLaWGvTtPXMrbIot8Ce17AaaI+LWKJDUgibVhO2oXRLkVAfNL8qhUTbWly4BHd53OKeWoJ0+YsnaPcSIZq4vdYvKBhmPCtr01z4zvOM7cyPiLmNW7dou4+kFJPo9VC1WNy08aeTWn/fgwKWNk8wYZcyAjk0ScRe+9Dr3rIoxR8TeTavOItqWfc0a1+fo7om4j4HITwpLgQlZtoU44xuJoQyXvToDI3VX8yJ8r6eezHuO5EinTT889m0VcyPiUol4KJ5jkImvY2w8bX5anokmH94h+VpMMj1DjTpsCv0wuC01xNmPSx1ftjov5IjYu2nh10lCi6pqoc2P2Hte4JZVd1kng84O60N//Y47VA9WkvTHfIdJzNGUI6IaecQk6mNI8xiV6oenuK1ibOIAl665Jqo64qZjXh1hDsFzbBKmvrHx5MSGKynryUqdeynhthh/r9IjqrRNvTOFfpj+mLoDl7lqtN8U4zNWnbj74utP6tY6vrSTrY8YPcr3c0TM36j02elJpDX8O/El5jfYnSMgyWz4QM4SzqRhd6CB7NwsSB9dRuPx00XiJY8D9ZuF3OvDMNqwEXw+fZuoPrwKuiakManyXC06Vu/3nHW4dqjl9Jm1ADeMtlmmCRXNhUZa2C/BDYRR0ucpb6sYmzi6psHkFhNSOZrXBJDhtUJ0ZdV/vWnx9MGTcSd0naAFi1xEsobgbp8iz/jN/GdLFu/YePLtvdN6s5ShrC2CYUi5aknHiaDjVmT6QCk9WTSpd7xqrrrusZ/AFajQUFeY/po5C59wPRPrhOTv1XFdehpMeIlTN3OZcHDyd1ghaAkDHSkhOMVmM8vVRdYx4NyuiuWaAgmQ5R93FQgTAmbntNA+JqsPSeUdAiNwS2JAKORJwEOCYslzGJxqDgZ+t7SHSDlMtq9IYqBZOLjTlOyYEDmSdZ3XARZpdmPaSqEffAPAqhmqiDAiKRE6XZ/MnDYS/caC6Or/artkneXZGwHI6YHh0+qe+20VzCus4Gy+5Nmw0uZHDI7MO4i59EqrvngyT5kfHDHNbxypj5B8CA0hYE4Fdz/wuaNr1HtdO0kdYAnjS4nYn0Zz6jL/O/MWd0sECVsn5t2BWsNHx5lHBBkM354Bc+mJ4ZnvCEts6sxb+gk+nEwQNpHyiSBlg8pmvWvKNcEEZWKisEcvhWM3EWAceYh+8sdOSBaJwqRowxrJl2tcIBLqgLwgdRpJo7mfKtcw2sV7TAY8GXiH3RTpuTStpAVo4JdajfDLuQVZ23OSRNVgUp1TXXXaXseeU7/k2kWgA/8s98ecb/8ouSqJDR43Na6SQZL4bo9r1Yfgyfy7mCSS4aBiOjgtHiTKUve5TRE26+NskpCMEQyIfLP7EcETuwVXTyHAsPnZVUlt7fPqnVygRm5cq6oEJGqEHu/lwxrmxMPGlvOg2oWrkhgTVK3k5yAuAKyM6xAu2LBqS1v2tbaBW8LvpsNBmu6THH5ufYzbKsYfEdv4SLgEaaEq60pe47dm2TVCwKgfTJ0GtuCJ/pQgkVyJy0OXPeadW8+OjDSNLvagzm/N88G4rWL8cUEg4fSHTQNJsPRuw/FbtNwaydqIqsRUgfyPqgc1ZE7nb0FUZFWcMrvgrBFdg0TMAJjEc9gODPYSb6uY8yLAuIWB5bRJRXHIDsyRbeJtLqMc0UmZiT4bNWbd0RyixtaEJN3VCL/N/k3y7bUQMeBh2TwgGeLGiI2fZEBaKl3qbRXbwKrLN9mgSbsJYeBDjgEMA5Qdq7vUEc8cFQFTneEpcJ6UnbBOJYHxH/0pmx86+bld37SxsV0TEZtLHQEb+GNmr7XeGPL9PtT1top+ta/rLfPqwchltgMz7KLPrPN9XxdK5b21yLwLpcRNuCLWeRIRmbdPgxGv/OsLfWNNRMwQsfj2T3djkZh+iaXrbRVL7Nsm24w3EJ44ePzgfonU5p3zOT3tN0J+5E32aQ7fMjUgbq4IPHX5pQlKIlcFXhZV19c59GOjbVgbEQMuPtL4DLNTr34CbHS2xcfWgEAXgkUgwt0Vd0XcFldf1kjEDDrRLvg04sM75EqW1U+gACAQcAigH8ZVDX1vHcHi8030HUmL5hYss7XBXCsRbw3w+HAgsGMIoFoghe2hSbhBtx5SbuEgBxEXAhaPBwKBwH8RMOMx7n8YOLn4lqi+KIUIBBEXAhaPBwKBQCAwNgL/ASx5/XuDCjqwAAAAAElFTkSuQmCC" width="177" height="31" /></span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">determinant = simplify( det( A'*n_t + B'*n_x + C'*n_y ) )</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">N_x = solve( determinant , n_x )</span></div></div></div><div class = "S12"><span class = "S2">i.e. there is one real solution and two complex solutions. The real solution </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="41" height="20" /></span><span class = "S2"> is typical for parabolic equations, since it represents the infinite speed of information spreading </span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="49" height="36" /></span><span class = "S2"> . The second component of this normal vector </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="42.5" height="20" /></span><span class = "S2"> would be obtained by replacing the equation (3b) by</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGIAAABICAYAAAANkiBeAAAIcklEQVR4Xu2cBag9VRDGf3YrKnaDYmKCit2J2N3dHdjdYqOY2N2KigEGKiqKXSgW2NjYySczct6+s3X33vv27t0Dj/+f9zbOme+ciW9mdhzaUQsJjFOLWbSToAWiJpugBaIFoiYSqMk02hPRAlETCdRkGu2JGCAgxgUWAHYE1gXmBT4CHgJOAz7scC0zAzcAswCbAK92+JxG3JZ3IhYFjgXmBs434f9hgOj3GtsDT3QgjSWA+4A3gK2Arzp4RmNuyQPiGGAe4DDg82DVum9r4DrgamAf4KeSUtkcuBm4GDgY+LXk/Y26PA+IrMXOAdwIzAWsB7xYQjJ673H2cxBwbol7G3lpFSCmAC4CtgW2AG4pIaGpgCvMNqwIPFni3kZeWgWISWwn7w6U3dWyOVJLGgLxvUZKt8SiugWEDPdJJd67ghn424FdgO9L3NvIS4sAMTuwHbARsJi5rneaatkP0Ik40lzZNCFND2xgtmQZYJrgQrnCj5srKxX1WyMlnbOoLCAUP0htXGiu5VnmvuqR8pikjjQk5G1MkMnXSX3tARxt98pDeg04FdjL7nsAkAd1ip2SAw3socIjDQj9fkvgEuBNUx+vB5KZCDgT0InQWB+4NyG56YCz7SQcBVxmu90DOQWG7m3pfWuZwX/UTtlQxRVpQCxsxnRW84ruiWxPqSQB9VnEfZ3MgNKuP9wA+dOe4YHcO3ayPrXfh+DKblw5TEciBkQokGuBfYEfIkKRCjkHeMYiY+l6H1JpOgGPAbsCXwZ/80BO7uv+wM/B32SLrrFAcW/gx2EBIwbEgsBtwPymkmI7czzzko4wox0KNIwRkjs7L5CT7bne7In+//UwA+E79t0MMi4UdjKGkFqTW6qRJPPC+9YAHkkIugUiEIj4pRNzdqULe3Izxs8H9y8LPGUuqQTrNkCXeCA3IbAZ8HYCCFd3MbXV6MORVE0S0OmABHKp/ftLhqGOBWQOhGjypHrxQO5+cwK+DZ4dUiZlI/U6geQx04aAZKF1vWT2UhtMm++f5ISTQIS6Pw2Iqc2j0Ys2BhTchcOBEAmYpC/c01IeQyfvr+BGgSTa4ztgU6PH6yTgvLmEMdMnibTB6sAhwGyAnBDxciPAiBnrPPXgelwGXYINd7UmOxMgb2s1YB3gQVtBeNqUw9A1PmawE6h45ADggtiuyZPEGP5du/4MYE/gckBxUzIOWsUckd/Ndr4QzjcGxJLA3cDHFtR9ENywkHlJ+pUydm9FFq9nKtA7D1D8IbC+ABTgiTZfCpChftbu1e8VVcvNVcStn7K5jTHEgDBmCtebnFOoekdphBgQ41uiRrZCeQLREkrarAkcajGFBO2CjAlBx1TJHiWUFCkfD4gyudV2iigRcUprWywxpeUmpJoGjWvymOkbs4lPZ+yKVEcoLbKW0JQnkMBXtQfLM7rDOKVYgBezP/NZsKdctwjDcMiAvQKIa5JhL/LMsdz5sXcr364s5cp2kpXscgYhdr0DoXUrTBC78N8owr52Y/F6j/SmqPI8prYb7+vXM3Y2VS2aR+xy6MbXEohQP8YIwm4ILkxUFX3eqJ1Z9EYg9B6L5O1Dj3QULdSvE+H5bRnmXpXO9BsId2rkJYrql7ufNSY1l1a0z6g4ql9ALA08DDzXoNIZd/Nj7HMMEKf/V4pVrvQLCGdV5YWJFpcvPchjYqP2RfPLKyxSl+X0f/QE9QOIUDcWOcKDANC05j3Kpc+igsK1ZOVv+uY1DYJwy8zRyUvt8iKFE6Gzchcgb2sEI5E8EaPIqDKz68G18s9VWFBk9NNYK80rvmiRgkCEhj2afWyBSARWRRC3QmwHIk/dKuMpCkdMgzKWKsgTKThi9MNGFFzbQF0WekB5qsnJPuVudgsK61ogugB5mNfPMtYhqyzOTtxblNBsT0TnqHj+JEprW9+H3HXlVkSNy20XMRgdLRCdAyGWWvZBtP37ll4W8zpBwFSLSTjZyo5imc7/394C0TkQulPyU/5+JxO+vCkNlRap5kv5F+V1ckcLRK6ISl2QVeuV+aCiQPSqj67UKgfgYuXrlRpWABfL56cuoQgQveyjGwDZlppimK8vQo2XshG97KMrtcoBuFgbW+pJxdcqFxUpKDuhGEJF3eoDGVXB4camyvqq9NFVeW+d753TqjWkpsKhtKgqVJQWzq1rKrvAKn10Zd81SNe7OlftlwCQmlINcWqrQREbkSWAKn10gyTYns+1m0DkcS49X8wgv6AoEFX76Lzm1WUVa/WS/pRjoP46GToZN+V2h2LkAdGNPjoX5OJmxNR3kXZ6PKVatDylMSBlAaG/Ve2jCwUVGvYTAP0kvQevqy2afhwKIKr20SWFlFfy77ntHayKfKi+RpB2IrrRRxfbrWr1ElsZ66vQNz1uAl7O6MtozAlILiQNiKp9dGkCS2vN0jyUy1VZpgrQRpSsN1b6wcLSgKjaR5cmu7QmFo9G5SWpfztsYBkGHFLLaar20aUJz3vv1NLr1dBKsCh7pWpAnYrwu1BDAYIWGTsReUbVheMFU2U+bOLclL7HsRygjJZOyVX28S2VZQ7liAHRjT66NGGGFXLqGtJ3/OSq6nNyeb0FjQYozUZU7aNLE1rITclNnRFYfphVkgsqDYiqfXRpQOh9/gk5tX7phKh3rpOPMzbqhKQB0Y0+ujRB+WnT3wexg7QnGyCL4uhGH11s0uHXLVMLrnqy2ho/NI/06/bUvRVWVdSqAdX3PtrRx2ZGCdvVnZrCO/1ob2NB69eJ8Ko4BYqyEeKU6tYCMKYg9wII94zkqoo7UtmhPnKiANCrGv4e01XX8OW9ACLMO/iSVYKorxaoYb4FIbIRegGECDzVfaq/TBUM+iKZPoBSqAa0hpu1L1PqBRB9mXjTXvIv684tZ9Wm1CMAAAAASUVORK5CYII=" width="49" height="36" /></span></div><div class = "S4"><span class = "S2">The two complex solutions </span><span style="vertical-align:-7px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHgAAAAoCAYAAAA16j4lAAAFYklEQVR4Xu2be+hfcxjHX3NrLCQJS5kilKYskQk115ZbuW5syV0uDZsZhpGNQhSRS+5muV/+ccmlWfxBsTSLlWVkpJnbRha91/Osz45zvufyO99+5/vZ59Svrd/O5/a8n8v7eX/ORpCeqC0wIurTpcORAI7cCRLACeDILRD58VIEJ4Ajt0Dkx0sRnACO3AKRHy9FcPsA7w08B+wPHA281f4S1WdMAFe3VdU3TwBeAT4DTgeWVh3Yj/cSwO1b9WLgJOArYBbwa/tLVJ8xAVzdVgP5ZgI4H7YdgaeBXbqQZofiWQngTRTga4HbgrOfYcxwFDAFUJ0ZAzwP3Ah8OxQv6+DYuhF8MPAmsK2dZREwCVhecLY9gfnAOPv3N4CzgV+AscCVwMnAN4aD7PxPEzsVRfBmwJHAY8DvwCnAauBuA/YvQIfSo3cuBf5osoGCMWGrUXXaB4FpwJqqA3q8VxdgTbUb8AAwEXgYuAL4s8caOwB3AOcBc4GbAQXSLcAyYA9gd+A3A/udJufqlaLdyCuA6RapLwD60XM1cDtQ5q1N9jWIAG9tAXChsWeBVvbcAMwBzgQUVMcA1wA/AHsBTwIHWUQruGo/vQA+DHjfvFKL6+/PAv/aKpOBp/oEcO2DDGHAeGBhzfGzLdLCYTsBz1jmqyJwbAPcAxwOKPscaFG/0ib1LCLQlbJbB1ieqJSjZyZwZ6YOOMCqD0ozSuGD+LQFsGqnbLEWOA34ssQYo42pHwF8DJwDLAnGhACfCLzaxLhFETzSAL0EeNcIwHeZBZyIKRUp1axrsoGOjmlSg13BcsK0quRsITG7wOq2Z0cNdSK2nXGgz5vYqgjgMN1cZCkknF9s8T4D3hl2k/W7OqYuwLKjugn9VHV4dSOPA+8ByobfZ4xxlDHzqg6Ta8sigEXfXwsYdNZ7xO5Ub+QIYtiNvKsHuoNGskKHnwo8UeK5WwHzjPUXOYQ6grtqOEwtgCWSq0972/q5n/rhXREB7OlUdfV44JMSgNUiiSGrpcpziNYyZF4Eh+nmfuAqIw7hnmOuvzpn3RTtHUdRus3ivQ+wwDQFMe6PMi+0Un81Zx7A21vBV+rdFOtvE17g6bSKwKH5nZD1tf4WARzKaOrRPsicOKyPhwIfAmLdNwFi3RJCpGz9bexaDFv0/1TgiybW6/iYsOPI64/ztu8ZMM8hFHTXWZ+dVee2NBFFWVUfFbhapj1cDlxvyqKEKamNuRHs7E11RAz564L6q1+fa2KHwNzC+mVpsA6mesNHTU99KRBJuoTZUPvgsJ9VXZXC92OPA4b1VffFWcUr/Hcx6MtMk/YWyhUz3QWIff9sa3ngSRl70dfPS9GebvIEjNC7fI7QC6WfSu2Sd+n3ahteNxUs7PFiAtg7jl3tUItLhA7vQA4B8gSMvA4im0mVAVS7w/ZqAnC+XQRt6MHbvi7cHJgBKAtIyRHIn3YJzUj2ImCVhv2TIEW1WiplSd1qbXjaBlgTy5PUIyu1iCmmp30LiLUrMzoD158KKtXg9bW3V4puuh05y7Emnu9sk7R9jdh0b7GNc91bdwC6WpRoIjKr++ONnrYiWARLDbv6R6UK1YxH7OOALAuPzdjDcR6v4yJ1+9lFxEapuc0IFrgiZscBZ5mmKsIhuU76qlL1sH5ZOBwI9HlNV8IOsCvH7E1fqyla111+laX+7CFrvwS6Fn4Z0G1JVu7ssw2int5bJd3gidQWfk3TVoqO2podPNy+1j+rXQrvkP+31QRwB9Er2ZLqr3jOvaYv9Hw9ATwYACtSpRbq+zh90SoBSZ9QlT4J4FITDfsLrnXrs1oJGbfaf4uptLEEcCUzDe5L/wGYCEE4fL2P5QAAAABJRU5ErkJggg==" width="60" height="20" /></span><span class = "S2"> most likely manifest the spurious solutions created by the non-equivalent transformation from (1) to (3). The system (3) is thus </span><span class = "S15">hybrid </span><span class = "S2">since it does not fall into any category. If we did not know the type of the original equation </span><span class = "S15">a priori, </span><span class = "S2">we would conclude that the original equation is not hyperbolic because it has for sure less than three real characteristics. One of the messages of this exercise is that second-order PDEs should be preferentially analysed by method </span><span class = "S16">a)</span><span class = "S2">, unless it can be proved that the transformation to first-order system is equivalent. Two common cases where the transformation leads to equivalent first-order systems are considered in the next example. For more details refer to Wesseling (2001).</span></div><div class = "S4"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">1.4 Steady 2D diffusion</span></h1><div class = "S4"><span class = "S2">Neglecting the variation of </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">&#981;</span><span class = "S2"> in time (corresponding to a steady/equilibrium state) leads to </span></div><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="143" height="40" /></span></div><div class = "S4"><span class = "S2">The discriminant</span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbUAAAAoCAYAAAB5JWT0AAANJ0lEQVR4Xu2dZaw1SRGGnwWCO8F/QAjuBNsAwS24uwZd3N0JEoIEd3db3N0lLBosEAIsrgEW1zz5urPNyfjpuXfm3JqEsLt3Tk/XO9X9lnXNYcQVCAQCgUAgEAjsCAKH7YgcIUYgEAgEAoFAIECQWihBIBAIBAKBwM4gEKS2M68yBAkEAoFAIBAIUgsdCAQCgUAgENgZBILUduZVhiCBQCAQCAQCQWqhA4FAIBAIBAI7g0CQ2s68yhAkEAgEAoFAIEhtug6I3VmAWwHXBA4HfgQcCTwDOHr60PHLQCAQCAQCgSkIBKlNQe3Qby4NfBp4LPB04BjgisBLgC8CdwF+P334+GUgEAgEAoHAWASC1MYiduz9ktr9gTsU5HVc4PHA7YBrA0dNHz5+GQgEAoFAIDAWgSC1sYj13/9I4IggtX6g4o5AIBAIBGojEKRWF9GTAM8B/P8IP9bFNkYLBAKBQKAXgT5SeyjwxJZR/gR8FfgK8CbgC8C/ep+4rBu65MszVb6vAa8DPgn8vUUEsbw58Bjg9sBnliVq52xOBDwFuAfwqBRCrTH9EwBPSGFai2ceAvxjxMAnB66VcL0UcOr0288DXwbeC3wc+POIMff71uMAl0xh6yunYqO8hl4K/Hq/Jzjh+Ybd75d06IXAfYG/Thhnrp+oh2LtvJzn1+d60Bbjun+cO62RzwLiGNchBEbpVx+puQBvDbwioSsJvDj981mToriBnwt4N/BA4DsrehNd8inG6YDrJrncUF+ZNujfNsh4OeCZwL2BT6wIA6eqjK8GTlaZ1K4KvCWNO2azOx5wY+DRCcfnAm8D/glcA3hw0rlvADdZkc4plxurIWoLip4H/A24JfBw4FvA3VeYi71Yes9WA495z3MvE/e3i6RiLo0jjdObAt+d+8Ejxz9t2lfultaKFdWvHTnGLt8+Sr/6SE2gcpWf/+wm9aEN9M4MuOm4MeqtSXLfXhHCffIpilWNrwHOCNwR0KIur/OnMn6LRPTm1nRpnCibOHjV8tRcqG5w10/jDt3s9BoflDze96RN3qMS5SUJOGf/rtG1lirTmwEvAt6QyC17mJKdXqz6o0zq2C9WokSnSu9ZI8Rr6HueWzz1Wl2+USIKn7c0UjNNcedkCGsQ5CtI7VgsRuvXEFK7CvDBHoU4D/B64ELA05LV2Ramm1uZx46f5euy+gVWT8bzaJthNGXX4jbsuDYPLYcHtYT+A1yhEqmpV27Meh1ucuLzgeSRNHm5+Z25uVtR+uQeA+nsiRg0IMaGNMfqR637NYhelUKPEv1HNgY+H/BmQH1qMpxqzaPmOL7ne6XwsIbF1RdAapko9IhNGWhASLgPWxCpGSHSUDa185PkFJwSeHYynIPUDmnpJP0aQmoqh+ewDCO52P7QsCpyKbvhyaVZQ32LOMvXZfWfIoWLtPrcoN14DRudPoUcn79CQhMXvWtDpubSDM9Y3FLDUzMc/Ubg5cCX0nm+IaSWw5XOTaw1ppqu06TwjCHJteQebgC8NeUA9TR/tiGYoV8jHnqeGlAaBOatl3zlsNAjgLOlMN9+e2pGju4JvAD4YQIve/ZL2Zs03sztmRf+aDIo85rRMQhSO/TiJulXH6mdMHlexnqflHIB/25ZZdcB3pH+1hSmXOLiHCrfmdImevmkjHprubjCpLP5kf8mAVXYOwF/XHhc3MXv5unCspjD91uD1LL35ybneOdMpGby+xap60qTLpi/NF+rHu33xlhbV4+fvE8NqC7ZzLU9LuXUDFV+v/ZEKo5nEY+ehevA96xh5NyX+O6WRmpNryFI7f9RmaxffaRWbua3TeGTtnVR5qbWYmkMlS9b2eYKDWV8M+UXcxFEEyYWjiw1vybx2gnlSskzMAQiUdcgNcMqL0u5Aj2trBd9VrKH2DUO9E6awnMV9+M9H6oMX4u7/8tGUDmZvPn63y6z4AraHF62uMU5W+mbCTlIbZp6Bakdi9tW+tVHahcF3gWcNG3illLPRWp5UYxRiW0X/hD5LAJxsz0vcNeUO3RD6pvvtnMbg8PYe3OYTw/cKis91hqklpO6Py7yqkNIrQzvGlIsu7SMlW3o/XoYWeahv+kj5rZxcg5QfesK7+b8ruMs2TC8YMpVmbMy/+lRniC1oVrUfN8cpFY6GkNnVyP9MPRZbfdtpV99pJYtR88CNeUByklt66n1kUQTANsSR5ZvMzSmJ3MG4GqpnN9QoonmHP/e9qXt5++VS5K2YMPcg7KVG/xUpS6LQzyvlytgVVA92nN0eB/ZuLCYwlyDZDP3tZekVm5YXfhuu4bmxszxLcTw/UjU5v9+mh4apLYd+kFqh/DbWr+6SK0s/nAT9PzVXzreW5lTswDhndu949l/XcrX9rBfpaIQE/xLOkw6FZxcOm7Bj4UYFnF41SA1ScscnVWwzyrCa+VibTNCDHua2P/5jrYXK8lqzaTmfqEhaLGUhJZz6OpQLVK7bDr2YEjTytYah9Fr59QsEDOf6LEBqz+7IlhD1+ocpDb02Uu5r4p+dZFaGRLSS7GQoOvKVYTfSxvmEk/tl/Mv5SsPlXuPScrrJSK3ytG/v70lD1JDIUqFHjrelNxFPm/nppTDRjVILefoLEeXoMqNqJStqYCoLKIYEhEYis+S7tsLUtuLSEc+uuNXKFzvZSeXGqRWVoD6/moZx7VJLRthznFKp5wm3VwzqdWKelTRry5Ss2WL7a8uMEC5SqHen6y43yxpV2mYSylfW7VmJgFbO+WE+Bxi7QWp5bDjiTfCRm2kZn7MQ+aeO+xr+aV17XkgQ4ebh/N9rgeObXPVlCcqiyiGRATmwH/uMcvw6lye2tyklsNCettWZm4arZuk5rlHW69JgEO7YwSpHTrru+R8atNaqUFq1fSri9Ry0nqI51VuynZFsLqrrfR/7g1k6PhDDl2X3lwti2zo/GreVx5qtuOLxT/lZaGI782/eSDU8KHhSQs2LMPvan22eeK/a95Ni7UsouiqDKyJx16PNSWntqRjMbmvqSFijRybdm9eGjRGdDybaCOCSwBPBW4zsgo4wo/rI7Vt11NV/eoitdzst8/zygUCWuPmRAzbaZ2Nvea2NDfnk+XrOnRdWiBra8lUypsPK1v4MuYaUu2nB+s5tzJH1/bsJi9l6IY/Zt5D7q1hXQ55jveUR0e6jCP7EurxLi23OAWrjM22xVxDMe66r3b4scacNseYI/y4lurHqvrVRmqGqOw0YUFBn4dS9g7cpkXWXpLaUPkOQmjMxTW1UCS/e9uD2Xy46SsNpbd7UEltaLeQnKtZY26xRk5tDrJwzCC14chOrX4e/oRpdw7WrzZSs7mmZ1DMg3g2q60VUS4QMOxgM2MrogxXLv0aKl/Zj09Q9UiaDs0uXd6++U0htVxJaXgyH0hvek45dlNXGhsfq2t+GqRvQRkONZ/jM2tUxfXhUuvvrjMLKzT62jqrlAUzfYZkrXnVHGfwplPzoQPHOqikNhCeVdw2WL/aSE239X2pu3VbZwybcrq5WEn3O8COI2tp6DtEvrJzul3i28Jrq9CInklOITUxtADA8HTX97PKsZsqNsvNvKtQJHuFhkRz7801YW+OyQpaz+LdEDhyY/I5RGlRyRo7qgzedPbhpQWp7QPolR85WL+aSK20Ko9KlvFmDzorVUwM+/20HwBHAJ+rLMRcww2RryRs5+H3u8wZLr34ZSpmZZi1z1vyGZ7TkaAsue67vxy7LT+bqyetMm0yHvyWnUcQ7Km5V4ezp2LZ9rvyg6l24y+/jF7mpS3C8NM7azoXWfZQnXLUpDbWm+Pl40bb5PznnmNZIavRpre+i1GhKTiO0q9NUvPfLeF3A/frvC6+B6TzKHouniMwTGQVmyE8P6Vhh+6jp8x0H36zKZ8fNvXwpF01vDyfduH0KQ1Dan5MUPm0qi1R3tWr/HSQh6ftEN/2jTLDhYZhJRgvC2jEUONm8yqNA/NK9nW0NZfhxhJPdcswt5WXVloapjRM52UI3KKei6d/X1JV4Fh9yId21S1xlqh/mTwzMfVzNHZ58b+t6crHRfw006dSGmLzG3h7KY/r3LXsZlh+VNY52IbNowamSdTHMV9iry2DUQzz+6Y5dBD8UoaX+44VpB9Le+8xtR+8svFG6dcmqR2ePvfhBtR0CbbtjwwzGkpRcddkTfTJp8x2B3BjtbWTCzQT3sr0YPB075O6QegN5cv3bMhGT728Sq+r/O8fbslztRX/NB2qVRdtqeWmruGUP5roXIwU2P1EovPMXHnod7CgC7nRKIfym3/OH2ZVJkOvGllr+Q5hhtNQqV5F+ZFL9wW9IwlkP66yMXTf8/erOnPM2dS+aEifjGv++2j96uv9uGYwYu6BQCAQCAQCBwyBILUD9sJD3EAgEAgEdhmBILVdfrshWyAQCAQCBwyBILUD9sJD3EAgEAgEdhmBILVdfrshWyAQCAQCBwyBILUD9sJD3EAgEAgEdhmBILVdfrshWyAQCAQCBwyB/wHvbJ9WDG56dAAAAABJRU5ErkJggg==" width="218.5" height="20" /></span></div><div class = "S4"><span class = "S2">implies the equation (7) is </span><span class = "S16">elliptic.</span></div><div class = "S4"><span class = "S2">Using the same auxiliary unknowns as in 1.1b) we can eliminate </span><span style="font-family:Cambria, 'Times New Roman', serif; font-style: italic; font-weight: normal">&#981;</span><span class = "S2"> from the transformed system to obtain the Cauchy-Riemann system</span></div><div class = "S3"><span style="vertical-align:-33px"><img src="data:image/png;base64,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" width="157.5" height="76" /></span></div><div class = "S4"><span class = "S2">which is equivalent to the Laplace equation (7). Computation of characteristics</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">A = [ 1  0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">      0 -1 ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">   </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">B = [ 0  1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">      1  0 ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">determinant = simplify( det( A'*dy - B'*dx ) )</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">Dx = solve(determinant, dx)</span></div></div></div><div class = "S12"><span class = "S2">does not reveal any real solutions, so the system is </span><span class = "S16">elliptic </span><span class = "S2">as well.</span></div><div class = "S4"><span class = "S2">As we saw in 1.1), with more than two independent variables the transformation of both elliptic and parabolic equations creates spurious solutions and the resulting system is therefore no longer equivalent. Thus it is very often advantageous to analyze the type of an equaiton or a system of equations with several independent variables on sub-spaces of only two independent variables.</span></div><div class = "S4"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment active'><h1 class = "S1"><span class = "S2">1.5 Korteweg-de Vries equation</span></h1><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="185.5" height="40" /></span></div><div class = "S4"><span class = "S2">We introduce the auxiliary unknowns </span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="101" height="36" /></span><span class = "S2"> such that we can form a system</span></div><div class = "S3"><span style="vertical-align:-52px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZEAAADmCAYAAAAUcbiaAAAgAElEQVR4Xu2dB/A8VZmu31XWHDDnWLrmtLpqqVd0RdE1oZgzZlGMF8UsmFAvGBDMq5hBxXwXAyoqrlKwKiqY9iKusUQRFcV866G+s3tsOpyZ6Z7p6X676l/Kb3q6z3m6p98+X/w7eTMBEzABEzCBJQn83ZLf89dMwARMwARMQBYR3wQmYAImYAJLE7CILI3OXzQBEzABE7CI+B4wARMwARNYmoBFZGl0/qIJmIAJmIBFxPeACZiACZjA0gQsIkuj8xdNwARMwASWEZEdJN1E0u6SdpZ0BUnfknSYpAMl/cxYN0bA12Zj6H1iE5gngUVEhH1vLel5gerlkr4g6e8l3V/SMyWdEOJy4jxxbmzWvjYbQ+8Tm8C8CSwiIueWhHCcKulFkn6doeMNeG9Jz49/+0j687zRrnX2vjZrxe2TmYAJJAKLiEgXtRtK+rCkkyTdT9LJXV/w52sj4GuzNtQ+kQnMi0CfInJpSe+QxAPrdpK+OC+Uo56tr82oL48HZwLbS6BPEblIiMguku4q6UPbi2VyI/e1mdwl9YRMYBwEhhKRB4SgjGOWHkUuIr42vh9MwAR6I7CoiLD/1SU9XNIdJV0twnvfIumD4XhnJXIfSYfGKJPT91HZqF8s6dkV5/t5JL0yjs1nL5T0195mOv0DLXNtqlTOGRF4D5V0G0kXlnRUXMsPSHqcpD9JeoGkP04fqWdoAibQRWAREeEB8wRJz5L0TUkIASG+55e0R4T5Ihj89y0kHZ2dnOgt3oDfHH/LRSbtluz2t7I5rOuyneXzVa5NOtglJb1U0gMlvUbSayX9UNL1IhqP3CC2R0t63cIj9BdMwAQmSaBURBCBp0jaL1Ycj40HTIJyIUlvknQ3ST+WdGdJx1WI3VzS5yV9R9I9JB1f+TxFEP2m4fNJXoAeJtXHtblECMM/S3qSpENixZGGx98OiLBuB030cNF8CBOYCoFSEeHB8V5Jv4gH/LEVAGeP/JCnx+qkLsT3LiFAH423XfJN8u1B8fBq+nwqzPuex6rXBhEir+cZkvaPpNHfVwZJMunbJX0mVpw/6nsSPp4JmMB2EigRkXyVQZLhcytvqcz8HLFK4Y0VscFnclqGhPPwPf7V+UNyESKhkcTFP2wn0rWOuo9rc6O4Zr8NX1Z1hciE0krkjWHSZF9vJmACJlDU2RAH6/uDFeaqI2u44Qc5KFYYvNXyL3eKX1ASDyDMWHXhv/nnD5b0Vl+bIgKrXhvEG2EnkAE/B2Lxu8qZzxUrFPxeT47giaLBeScTMIHpEyhZiWCiYgXSZsqgCOM7Jd2sQSSI4iJaiwisOn/IVSS9W9I/OFFxoZtu1WtzUUlvk3T7Fod5HvCA6ewTC43QO5uACUyaQJeI5OG5TW+qALqtpI9L+pKk+0bpkxxc8ofUmbrY7+6S3meb+0L3Wh/X5rphyrpqTURdGkxa7Xw7zF3fXWiU3tkEpkfg8vFbIBDlnyS9InzC2zzTFPhEpZFj4qWe5/lfuibVJSK5mek5DaC6/Bmcgwq/FGes84dcIErI41i3zb3riv3P531cm3TjfFXSvSPnJx9BLlSsWIjKywtvlo92u/e8eLQ9wBRLqDM5TNyrzmPa7uu66OgJQiHIhEjF/wwzLw9c2l8QVdq0pRwufL2kRZSGyJ8t7reHZW03vhxtN4iG7bPtBn5tfKzc35iuyfc7OEzdBFS1Tq7t89zX0SQiV5L0Lkmo866hYvkx82NU/R3AZeVCTgL72eZeflv3cW26RISHJuLBueaYAEqyJT8ofEX8/7S1rcrLr6D33CYC+bPqU5JInv5pwQQuFukR3Ef8jkorRiBY3Hf87nhh4YF+RqXtBi911VSKgiF17nLeyBljzJz3qZJOb1PItiPmUVd1DnNWIZwAn0lTeGhbyY2dwhnP2+0Twx9im3vnNT5zhz6uTRKRutyea8QNzI1/pxkmgP6jpFdJghEVqXnz42Xp+44cLLtBJ7bXFSPMHRNwU4BRPmUexI+MaEZ8xmkrFRESsl8fZiXEJD3E87YbpEMQCfuTAVinxcE14xlNRZLarcucxZeSv4IILZZVKb8jNUL6V0lfaVHmXEQwaSFG2NlwwiNAlNDYM5ZrdUmKA/CZzCFXvTYp4IGs9KdJ+j9hoiHsFxMky3ac95eRdK+oVDAZeC0TuWX8gOHDmxiN2Po0HcyB4dTmyLOPFcER8VA9pWGCmKDwlfBi/YOIWt0xTPaXKlyJsB8RqpiW6gTrWpLeI4kXPUSEF5y+t/wltXXlXSIiaWlDOQxswZR7p5shNvS9wsaHGYpM9LqNkhyU03h82NMRHDaUlb9hVyYyi4x11BcHO/WZpr6lBL4mM2HJ/Fe9NnmiIedL5fu5L1gqs9Ej5j8aEkRLxrht+xBkgAmPHzDiwb1bDXvetjl5vKsRyH2DdX7d/Oj8pnge8pvB7MULc/6yVrIS6Qo0yk3ZQ/oqecbzbMaP09gjqkREAIQQYNJ4TBTmw9HCgVHLjxT8yC4XKxDCe8l2pmAjSzWOkyK70oXgzY8SK9j/prz1ISJ9XBts/fCmJhZmRTLTKYTJm3caY9cPZyrXifucFyV4sPLG7u0VyFSu7vLzyMPcl8ljW0RESlcA+Er2DZ8IL99DRE2mUlSsjHA9fLYOYamILI/f32wi0JeIDEU4v5lL3p6GGsc6j4sZizev80U+E2HrpVsf1apTZYB0zvTAYsVJ9CIvcdjmCZUnSfS/Sgfn/VYiQOXywyRdZ0m/7SIiQoQUqwuqpNf5odNE0vOD/64WvOVvPNupicdxyO9iZY1vBv/e4ZE03HX/FI3bIrLSvbXSl8cuIuntixtpU76q5PhfBPSy5sFcNKv+v9Lzr1qtmt8jeQesBhEyuGN7pxQQ4kEY6fUjygebOCulag260rF6v3IC+X1Y98DuOlLRwzgOkhKvWQW03cu5Baf6kpeCYoh8xVpE0BPBM9w7vHwwn5KVdu7PprYeFomzbBaRrss/3OdjF5GbZgmk2EM3YdZZp4jkJgts2oSd05bgIdlb3LckERFzoKTvNdwaq1arTg8ceDMOAhzwE/IP/yH3DW+qmB7vUGm5MNzdOu8jpwd2UwXyLjqLiEi+b5uI5L+NqoikZ0vdi8aNJdEbCBNVVwfaXEQax2IR6br8w30+dhHhLZcH6VxyIpJo4rSk5QGmrY/F0p+3ON7uCAS5ZyRlEr5ZZyNetVp1skP/3xCNT0docUpszEsMzcXMONyvsOzI6bfalJTbdZRFRCQXh1VFpO7+yIWhKy8vd+A3Fsa1iHRd/tU/r7OVdx112Zu167iln+dj/lzEu/MWPuUM7dzGjC+EBmw0X8u31HeFN7i6t7w+qlWniBjOi/MUQcujFYveDksvtPcrIrBtItI2qfy33WX6LSqtZBEpuodW2mkbRSR/202Tn3rxxdTPpstMlMIv6/ZbtVp1XkKIFQhh9XSXzDcyoCl2unNhzsFKN6+/fCaBdYpIHhG17ErEIjKTG3fs5qyZXIb/nmYKmexaBeaROtVWwatWq85FiDBjTAjV1V9uGpm6sI/lHlyniCzjE2m6Dwj0IMMeExnJ3QRnYLZN2+ArEZyKvA1tcrtBZMNvcgxDnXsVESHKgkJsm9ow8+AjGHpbp2O99EHR9iNftVp1EihK9DdFxCUnb5fYDX1t5nT80nujickiPpE8wKOtQV8ye9aVLEI8yMkjoooCt0T7HRW5JDT7o3LI7h3RX8xlZXOWRWTYn4lFpJvvOkUkCUDdjzIfaf5AyB2TfVSrTmP4ZGQIVyPi8nOQsPu4tsJ43Xi9RyGBdYpIaTZ6Cnyp9nnCJMp9SaUFcp7IPcpra9knUnjRt2G3VURkG+a3bWPMe6u0mYny/fIQyT6qVacmY01VG6hhRngvtc3wlzQWxds2+CMf7zpFhBcFHvzkdjSVG8lzmqqrlfSSc+WGEHAaA1KRgppbXeas/J5urFphx/rm7l6LyObY152ZrPBXR15IKhT655odUyG+agO2VatVd5X257dKiDENkN4QD5rG8tzjQrv1o0kmxK5Vah/mLI6R53LsFmHm+bGTyQsnfLVAY1q9f62haCovQaxQMEd3iUhRJKBFZHP3t0Vkc+ybzkz1VezHv4xioMdXdqRnDmakW0frAkrFJ8f3qtWq84i46ltfXjEb0wT27BPHh2+yI1o1Yz2PuGoKmMjh5TXcqqHk3AusIqg9yEsPldDzAqH5SpnVKgVz0z3KSpYVDr43KncvIiLOWJ/s7e2J9UmAMt4UsyMjnbpClMZP/W2IbsHcxA+Q9gWYBH6fnXzVatUkN+L8ZKO+0f+O/6b8SaqYfWz4QZoqZvfJwsf6HwJ5RF5Xlnf6Fr4HTEeUbafaOQVs2ci3ojo0QUusJJs6IpKTxH1Icit9bMgXogkWKw+KhB4ZLTSqjbE4L/4Q/GWEoVMglyAM+oNQ+wsRY2VF8UaOS7XuptI5eQmWxsRWr0T8UzGBvyXAb4IfHG/7FK8jQpCNMvk4vMnRIDqtLvFylWrVqfgi4sS5KL7IGzDb0eELwQdiE9b679g8Yqoa1l03mjz4omu0basBTKyIFiuK/F6grwnikL/E5Ofhe6xWKNjJWDC9ssJGNH4eSayISBI1rCJ1HRLzFVRjzTCLSNcl9ucmMDyBPGJmmVLjw49w3mfIr09b2O3UKKVowV76iVThEHvM8iwpJE5BluLUWaLMcJNCTg3yGOeDSYaWlulNmjcRzCPUgcLW3lQ4cIxzmcuYxlAxeS6sl51nCqhgNUp1A5zsU94IFabiL0m4+P7wvdQ+1xddiaDIFJ4jSgTRoEDff0b71L0lUXq4s7H7lMlveG4kIbI8xpaJWQTh+GOYZfg7G2+6yfa+4eH69EEgmQ2wl2NaoHGbt3ERSD3H6ctRFzE1rtGuPpo8nLy1p/yiIsJbLf18eUBRmprWj2m7ZPQgxkFY0sh+9Wn6CFUCvDXQ3pW3hjzBiOucSog7SW18902q24Xoc52wW3sbFwF+Q7wk8+JMi29W+rxAT3EjSISERfrE10WA/c2cFxWRLmDJOdhlN0zZlrb/dhHt7/MUQsob1aaaTPU3m+kcKU8cI4qG3wShxVOumLytV49yIo+I6DyqCfCco+Iz/78pympb5sp9SFdFQn/poYNgEh1GPxuivBq3vkUkJeXQuAd/SV3oWEqq2jXaNhKJ4m14AnkyG2Gshw5/Sp+hgAB1sshCv322r/uEFIDb4C7kC/EbIq+ITpQkgJKgus1byoVJUYg8H06oWJtq59e3iKSBtHnzUzbmSVEfCKevt+EJ5BEmXc1ohh+Nz2ACJjAJAkOJSFOFUZw1B0XsM29fJLq0LpUmQXkck1ik8No4RuxRmIAJjJ7AMiKC04WyDw+VdBtJF47sydeE+YpMShJXWO59NwiQdUunOOyJ2Oabtp0aWo6OHuSIBshSG0ctzZNIlGOlR9g1CUpE1eGPyksY5D0smMYRYYo8JeaUZ1Lzp2rV0BFN3UMxARNYN4FFRYSVBM4kUvHfGqsKIhRI7ccBQ1o9DeCrUSbY43HYUF+I/bAjUtYhz5KkBSgrGK9MlrsL8pIdOPpeFteBoxHxgwmL7eI1HfFYpRAUQTmFasc+jrtHONn4PgJ0gHOBlrtI/pYJTI3AIiKS95eue5DklSffG2n3p1WApeJgZzRUmJwa33XNJw8/xBlGyYOvZyfP6zrx57r6P0RmEL5NeHZexTYvTW0BWdcV9XlMYEsIlIoIoW37xFtotapkmmpJR67UjatJZLYE2+iGmco7X7alz0QKq24rZ50qC+dZuZSMfrOk90cFUFaM3kzABEzgTAKlIpJWGfg2aLtIbHR1y0tZ10X/kEbPGy6VUBEk/jkWfvUbMV9lYGLcU9Kvag6bcnjaIucwRXKMnSP8+vvRu+KwSLKygKx+vXwEE5gUgRIRyWuotNWNyevY1znIcwduaTnlScEeaDL4o1gdsmLAjIVJqrrlAo6DnSCH39bslzc+wsG+YzjkD5FkARnoAvqwJrDNBEpEBFs54biUxW5skSipq+JjqslPqRTMWtQJ8rY6gWQipMcEq8RqIyXOkAt4V45IqhHE/xLNxSrEK8bVr5OPYAKTJFAiInlt/KZM2vxNt6niYxIZ+0P6vZWol0VvgLa6S2mViDmSSgHHNAwB3xdlN4jAI6LuiVHB0yLS7zXz0UxgMgRKRKSkMUnuVK8zVXEeygrzr201Mxmwa5pIXneJMvz4PfJWmWkYyaneJuD4VjBzkQNED2au0zdmUvZ6TZfLpzGB6REoEZHc19HU3YrENqr6EsFD3f1qzay8bpOLLvZ3H+UrwCYRyUN3m0pYkydC5V+SE6kigL8khfvOoex1f1fERzKBmREoEZE86qrOYU7y2hviDZaii7TwrG4kGdIwfpeaRDcyoslB4S3ZZpPFb8AUddXkME9hu02h2bTSJP+D6gOUtz4xhpCO2/S9xUfqb5iACUyOQImI5CGkNHnHXp4e9nndeZpS7d8QxZOLCDXqMWvhYL9DHI/G9fT/tYgsfoul8GvCcSnfTGHLtF07oqv471wg0udJQBCR6goxmTHbwroXH62/YQImMCkCJSLChFPC2bmiXSLlgonewfRBhjNNqvaTdHoDHWz35IhgMmFL5d/JSyBaCDOYBWS5WwtnOOIOfwSezpJUBGDVt1fkjBBlVS25nwsIZ350rChTo7HcBPml6Gj5NV+n5S6Sv2UCUyVQKiLM/2Lh76BhCRFbhOh+ThKFF+n0lXc5rOPF94kiuld8iA+FlYtDfVe/u6hvhakRscAsxUYEFowxI9YlH+ZmSvavy2RPDvk0wiaf2Ooz8BFMwAS2ksAiIrKVE/SgTcAETMAEhiNgERmOrY9sAiZgApMnYBGZ/CX2BE3ABExgOAIWkeHY+sgmYAImMHkCFpHJX2JP0ARMwASGI2ARGY6tj2wCJmACkydgEZn8JfYETcAETGA4AhaR4dj6yCZgAiYweQIWkclfYk/QBEzABIYjYBEZjq2PbAImYAKTJ2ARmfwl9gRNwARMYDgCFpHh2PrIJmACJjB5AhaRyV9iT9AETMAEhiNgERmOrY9sAiZgApMnYBGZ/CX2BE3ABExgOAIWkeHY+sgmYAImMHkCFpHJX2JP0ARMwASGI2ARGY6tj2wCJmACkydgEZn8JfYETcAETGA4AhaR4dj6yCZgAiYweQIWkclfYk/QBEzABIYjsIyI7CDpJpJ2l7SzpCtI+pakwyQdKOlnww3XRzYBEzABExgTgUVEhH1vLel5MYGXS/qCpL+XdH9Jz5R0QojLiWOapMdiAiZgAiYwDIFFROTckhCOUyW9SNKvsyGxOtlb0vPj3z6S/jzMkH1UEzABEzCBsRBYRES6xnxDSR+WdJKk+0k6uesL/twETMAETGC7CfQpIpeW9A5JiMntJH1xu9F49CZgAiZgAl0E+hSRi4SI7CLprpI+1HVyf24CJmACJrDdBIYSkQeEoGw3HY/eBEzABEyglcCiIsL+V5f0cEl3lHS1CO99i6QPhuOdlch9JB0aZ04O+UdlI3mxpGdXnO/nkfTKODafvVDSX339TMAETMAExktgERE5p6QnSHqWpG9KQggI8T2/pD0izBfB4L9vIenobNpEb7E6eXP8LReZtFvyqdzK5rDx3jAemQmYgAnkBEpFBBF4iqT9YsXxWEk/zA50IUlvknQ3ST+WdGdJx1VQ31zS5yV9R9I9JB1f+TxFd/2m4XNfORMwARMwgZERKBURoq3eK+kX8YA/tjKPs0d+yNNjdVIX4nuXEKCPSnpg5Jvkh3mQpEMkNX0+MnQejgmYgAmYQImI5KsMkgyfK+lPFXTniFXKk0Js8Jmclu3Defge/+r8IbkIkdBI4uIffHlMwARMwATGTaBERG4j6f0xDcxVR9ZMCT/IQbHCIFudf7lT/IKS3hirmLrw3/zzB0t667ixeXQmYAImYAIQKBERTFSsQD4TzvMf1aCjCOM7Jd2swSlOFBfRWkRg1flDriLp3ZL+wYmKvjFNwARMYHsIdIlIHp77OkmYq35XM73bSvq4pC9Jum+UPsl3S/4Q/CpVUxf73V3S+zqEanuoeqQmYAJTJEBC9W6R3nA9SUe0PBPXPX+sRLgCeKFn+1i89P+8cCAp8IlKI8fESz3P8790fb9LRHIz03PCeV49Zpc/g3NQ4ZfijHX+kAtECXkc65i8CCP+bdfA/bkJmIAJrIkAzzDy314R5+Nh/VlJWGV+1ZHPdnlJe4aPl2doSWHapnw8go5ot/G9hnnvKOlV4VZYVETwa+P/ps0HKRvM9+DI5yOgqnHrEpHc19EkIleS9C5JwNo1VCw/YX6Mqr+D87NyeW3klzw51HRN94ZPYwImYAKdBHaKyNGfLNDq4rySHhl5dReW1PT8rJ6cZ+K9w8eMEJBW8dNY/XAMtsfEKqguGZtE7X2XWInk42DsLw0xQUieKun0JkpdIpJHXdU5zFmFcAJ8JvvHiuP3lZPlNbWq5VC4OIT7Ulb+ieEP+UTnJfUOJmACJrAeArydY8q/Z5jiyYdr20jKxjyPL/k62Y6lIoJZiUK2X4/zIVxsPKvp2/Q2SV+Nl++6vk1UBuGlfNGVSHVOaXFwzXhGU5GkdusSEb6U/BVEaD0sy+9ITar+VdJXJDF4FLO65SKCSQsxws6GEx4BekEs9+iSWJekuJ5bxWcxARMwgbMSSNGp/y9WCHRxrdt4Ht4gnm+4AVLvJUxg+E9KRIQVwKslPaRBsC4Vkas8K9OztGoeQ2je3oOI5AuINn94UXRWWtqwYqCeFSpJN0OWXHtFciFmKDLR6zaUmaXR42PFgeCwsTzibyzJiMwiY51yKDjYq3kovrlNwARMYN0Ecn8uKwAqdeTN+PLxsC+WFh7qPMOwyOQv0CUicmNJH5DUVLUj9z83Rcv2JSLMjWc8z2bKWzX2iCpZiXAwhOBOYYtDmXG0cGDyOT7SELGVA75cKDThvTijKNj4+jhOiuxK+2ODo8TKGeu+Y3w+EzABE8gIdOW/dcFaVESIfj2gYxWRRAIxq+vb1KeIpFJUrIBwPRBMcJatVES6YPlzE5gagTz3ibl9Mt7GTpF0XUmsvgmrJFIGnyDh615BT+suuFjkv2E+enT4RhaZ4SIicq7wKxMZ1RalmkJxGUddy42qiLCqyRcAdJw9PMxt/9UxmZTfhzmusb2HRWSRW8L7rptA/oMpPXeJ2aD0WORJYXtmZYyNmwrWOFj523clUXmaHxpvhZh7G52PpSf0fqMiUPQQbRnxIiKCAx+TGS022nwQvMDwwnLVBj9LLiK4C0iZwHqEeCCK+G3YyAHZXVKdcz5NKR//MyJFwyuRUd2iHkwXgU2LCONLIZM4O/8Y8fNPk0TUzCXjrbHrh981T38+TgL5AxvT0aKRo4uISL5vm4jkwlb3wpREhAiub0eH2feEj+Zsku4Q4cOstHErPK4lfLdo/F6JjPPm9ajGQSBFqBDwQZTNP8abXR6FWGLHHsdsPIpFCeQvMdUeSSXHKnoIx4FycehDRFgdY4Ijhy/PJ8E5TyFcXo6a2nakueU+ocbCuBaRklvB+8yVQG5iaIrNz9/8iGZpCgGdK8Ntnvc2i0jy4f2s5gIwr3+LBO+2grdFZa8sItt8i3vsQxPIzRlkH+PwrGYJpz44qyZ3DT0XH39xAusUkTyQo4+VSNv92GUSS6QsIovfM/6GCfwNgVQ4tKmwaO4z6cojMNrtI7BOEVnGJ1IXMVYS4ltqZltZROh1/ukNX3ciCVJy4oaH4tNvgMAmHet5I7Ume3BuM8bGTDJuXT2jDaDzKXsgsE4Rye+lpmrnTOmmUTGd/et6M1lEKhfeItLDL2GLD7FJESlplJbMAleOnJG6hm1bjH/2Q1+niJRko3NBUnI2FULqejOViAih6VQeYaHQGLoraeWVyOzvIAOYNYGuRmmsVOiNQ+UFQiipHXfqrIlNb/LrFBHopTqFbVFTKRqwabVSIiJXl3RYFIisW82kK5mvjuraeJy5nx3r07vxPaN+CKQ3PqKy6qKurhiF7liFkM37qX5O66OMiEAeWNH2sG0acqnvIX0/Vc6lp0dKcM3No/lDnReYuorCSUTaOtEmsWrz9TGmovFbREZ0x3oooyKQ3vjqzAb8mF8SteT2jnIVLnkyqsvXy2BWzVjPI65oFkXV8mqrjHygPI/JMicn6eh4OckbUJHwyAqE8F1WvnXhu3ltLRJkqb6eC9ElIiMeUaT9BuNq8uM5Y72X28gHmSOB80h6ZZirmD/tDljOnxZ1s/jxUZAOezK9Gywg07xL8tpZpQ3zSFDlJeMysZogBJyNorVkmFMah0TApo6IVE0nQINyJbQc5/9TmuR/RY02arfRkqMpHymJSDrnyyQdGue7VlRep5YW9d7419hsSlIy6VKI0bWzpnmPe1YDEUhvkDxEeHvkB0xpE95M+fHSppSckW86GmugKzCOwxb5BLKh5m/uXTNoywWhavqtJT006l7RGfGoEAMqp7c9+BERVhlkpROYROdYejdxDOpnsYrBDFbSPz2v4tuYsW9zVtel9udzJJAyevmh0UehzmwwRy5zm3PeT6Qt7HaqXFKeVC/9RKqQKORF20SqQKY3NFSOLEmW/U2N5KcK2/OaFoHUYrSxXtC0puvZtBBInQ1/EBWcvzETWnmNrVZ/zjIrkeuHbQ97GXZjhIPqpohJaiRPPRaWX95MYNsI5G1Bl+khsW3z9XjbCVA/DfMPvWPqIqamyg+fDlUYbtSVA7WMiJCZSy17bMWpiTwg80byXSWGpwre89p+ArkztdGZuP3T9AwWIEAQxSGSfhtO7X9f4LvbuCs+GQIJcLzT851n/e+aJrKMiLRBSQ5J4p3vLOm4bSToMc+aQO5MxDlJdEvjD2jWpOYzeZ6Tu4apnpcM7gmirGj13RRltW10WIGz6qKLIaHBOGLMijcAABLZSURBVOQPlPTMlr7yZ86xbxHJoxnowUBomTcT2CYCeYgk43Z13m26esOOleir3cJ0z8P2CEnkE03hJSNl538xIrh4dp8g6S9dSPsWkbzWSmlcddcY/bkJmIAJmMBICQwpIn32uh4pPg/LBEzABOZNYFkRubwkMjGpwUJCC+G9h0cCFmn7hEjm1SHziBeIV+sR5QXB+LypQuW8r5ZnbwImYAIjI7CoiJAfgq8DhwsJWDiYsBmzYUvGhMV28Zo0+R0icQtvP76TPPKFcfyLpI/E918j6WldDp2RsfRwTMAETGB2BBYREfbFY0+tIBwuVJH8ekaMsLCXRgEx/lxX9TLfpxoGnCpLWkBmdxt6wiZgAttKYBERoSzyuyVdVtIDI8StOu+U6dtWD/+WcZxfZhmgqbLkDyMmua02zLay9rhNwARMYHIESkUkX0FQAGzPiI+uAknls9tqrVClEpMWschkBH8gzGP4QbqqSk7uAnhCJmACJrDNBEpFhBLCdG+7Rpix6pqh5O0dqXBKKWMyPOs2TF2k1B8rCT8LvdwxhU0h3nqb7weP3QRMwAQWIlAqInR2w5TVFjWV96TuyhGp1qOhwJd7Mix06byzCZiACWyeQKmIUC9r347s3dRK8nxRIuCYhulxzttLwoFOmZT9I7W+rePX5kl5BCZgAiZgAmchUCIieY5HWyOV5FRvq7ufQoTpDIdfZA9JF5hZiWXfhiZgAiYwGQIlIpL7OppEJDdPUVuGxMPqRp4IJeIJDX5EmMZSSPCcSixP5ubxREzABEygRESglKKumhzmqWgdzndWJKdW0CIgRGKRzY6ApF4jqXNWXVN6Xx0TMAETMIGREygVkRtHKO73I+HwpGxe145yJ/yJToc0lc+3JCCE7x4gaZ+sL3UqHU8P4EfGcf46cmYengmYgAmYQBAoFRGEAJPTfpJoGXqwpDMk7SJpr8gZYZVBGeEmAaHUCa1zEZHkRM9NZdTfwtT1qZLyw76CJmACJmACmydQKiKMFKc4Hb4QC/oOsxGB9T5J72hIPszDftNsq+VQbivp4xkKd5Pb/H3hEZiACZhAEYFFRKTogN7JBEzABExgPgQsIvO51p6pCZiACfROwCLSO1If0ARMwATmQ8AiMp9r7ZmagAmYQO8ELCK9I/UBTcAETGA+BCwi87nWnqkJmIAJ9E7AItI7Uh/QBEzABOZDwCIyn2vtmZqACZhA7wQsIr0j9QFNwARMYD4ELCLzudaeqQmYgAn0TsAi0jtSH9AETMAE5kPAIjKfa+2ZmoAJmEDvBCwivSP1AU3ABExgPgQsIvO51p6pCZiACfROwCLSO1If0ARMwATmQ8AiMp9r7ZmagAmYQO8ELCK9I/UBTcAETGA+BCwi87nWnqkJmIAJ9E7AItI7Uh/QBEzABOZDwCIyn2vtmZqACZhA7wQsIr0j9QFNwARMYD4ESkTkbJKuKWl3SXeUdDVJJ0v6mKQXS/refHB5piZgAiZgAjmBLhG5vqTnSLqKpFeGcPwxxIS/sz1Y0lHGagImYAImMD8CXSLybElXlfRUST/J8PC9+0t6m6S3SHqcpNPnh88zNgETMIF5E+gSkTY6V5D0TklXknRnScfNG6VnbwImYALzI7CKiJxf0kGSHijpPpIOnR8+z9gETMAE5k1gFRE5t6SXS3qUpCfH/583Tc/eBEzABGZGoC8Rwcn+/Jmx83RNwARMYPYESkTk8pIeJOnukm4Q4b2HS3qjpMfHSuQZEe7bBPSGkj4s6VKxA999gqQzJO0UK5k7SfqcpOdJ+rSkv87+6hiACZiACYycQJuIkB+Cr+NAST+T9LII8WVKRGZhwmK7uKQHSHpHx1wvKulVku4b332tpKdE/slJEUaMs54clHtIOnbk7Dw8EzABE5g9gSYR4e887HnQnyDp4ZK+ntE6p6SXxkqEP99V0oc6aOY+lJ0l3UjSjpJeJOnXkq4h6V2SrieJ0OIXejUy+/vTAEzABEZOoElErivp3ZIuG9FXH6yZBw51RObHhSG+FwwT2KVjRcMK5mlZfsk5JO0n6UmSXhf/+7uR8/PwTMAETGDWBOpEJF9lvFXSnpJ+VUOJh/0Bkr4g6X5hhmqDSdY7woR/5KOxuskTGPkuK5B9Q2Qwmf181lfHkzcBEzCBkROoE5FrSXpPmJcwY72pZg5nj2isp8fqAif5bzvmeltJHw/TFT4P/n++MZbnxj+vREZ+43h4JmACJgCBOhG5d6wYvhMO7uNrUCXTFGJQmiOSVi7vl/QwSadWjpv7TCjsyKrkz75MJmACJmAC4yVQJyIlJiV8Ju+VdD5Ju0o6pmOK54kCjqxsmkQHXwkRXrcqjPYaL1WPzARMYOoEMPvfMkz5BAMRzcoL+Le2dOI3l/R5SV+M5zmuhy9J+kvXfKoiUurcTk51hARhOK3jRKnO1s0iL+SzNfsziX+T9ANJ95T0ja7B+3MTMAET2AABnmdU6yDKFNP7+yR9V9IvJf2pZTznlXSvePF+jKQfFY79IhEti+WHvLpfSDpS0muignrng77gPDz7LyTpJpL2kLSLpIPDIsT5GreqiOS+jia/BCfCT3I3SbtJIvGwa7tp+EC+HbknAM+3HSTtI4mkxf0lPVPS77sO6s9NwARMYM0ELhHC8c+SHh1pCV2J0axS2J90hn9aMHCI/k08b7H6YCVipUA6BM/I20VyNukWfUayInYcEzFBSKji3lilvc6clXwXKau86jAnaurt4XxnRVL1bdRd07RyoZFVXdQVOSOsalBy8lNOXPON4dOZgAmYQBcBnpdU6XhFYQsM9qfKx7PipTsdv+k5WD3/xUKweAknoftT2Q55Xh1FcHEFdIlZ1/zyz6nOTt4eDQk5fl2ax5n714nIjSV9QNL344FONnnarh3RWPw3nQ5LHva5iewzISL5Mu4yUQ14EWVfBIb3NQETMIE+CFC2ibQHzFhdVToQACpyYJrHqnNE5L49ZIGVCAFIvMzX9WzCakQ0K6uTT0ZpKnL2+tpKXRu1IoJpicmT+Ifdj+UMNa6wke0VOSOoMcuqkg2Y9B0BPBuZ6CQp0iERHwlhwiQe4nAncqtPNS0Zn/cxARMwgRICyW9Lfhv+ibrI1XQcgo8IOsJvQdkotpKgpfT93G2A2Qwhqm4pbYK/Y9r6RMkkFtgnReq25gI2Zaxjw8OBg1jcJk5KBBYOJJZNdcmHTWNLxRfxg7wklnUICs6pL4dPBXVn5ePNBEzABMZKIJnlefMnwTqJQ+l4FxGRvGjtLSQdXXMS/CX0cSI6rKsIbukY8/3yMaAHdQFRtSuRZU7W9p3kQ2nysfR9Ph/PBFYlwEsUUSqYE/IXnsPCH0itOGzd+A+p++Zt+gTyZGjagj92iWu/iIikVcDXIqLrmzWIidripR4rUVuCNtYgKrHTgRYxYCMUmZd4Vi8kl9fdx7lINZrvSkrBr3J75NFepUmJq5zP350WgRS7vsisVu1tQ8dO3ur2jh8Xlafx/V1O0gsk3TEG44TYRa7K9u+bJ0MvW1FjERHBzE8011db8k/y7rJ1znqe7wgMgQBYj4iAxaKEHzrdy23Hz0WqcaUztIjkme1D2Oy2/9b0DNoIrFtE8tBG+tpUQyfvkkWpuCX0vO7d/IG97AvEIiKS9m17yOfCVici/H5YqdRFvaYiu39oEalcRBpfzoYWkatLwgRwHUlNdr153Yqe7VgJ8Fsgcfb1LeHrSdTaSgKNdX4e12oEih6oHacoFZFcHJYVEV6IXi2JaLC61hrpHIQPN2Xa58JJkBWrc0Tnb7ahRSR/cyMkmPyStozO1S6zv20CyxO4YtyfvKHVFQjlyOl+Xtaxuvzo/M1NE9g2ESlyindALTLhDSkiHJusyrz3+rK2xE3fQD7/9AmkmHzi+UmuOqVmyslO3fhWNn1Ms53hOkUkz9FYdiWSApravt91MTcuIl0D9OcmMBYCJRWk86V9U9z+WObjcfRPYJ0iwugX9YlUI8ZKvt9FaSkRGVuiH2GUX+maqT+fLIF1OdZLKkinPjt0+yRIpDTZdrIXZ2YTW7eIlHSOJSER8SBisLo6tojEDWoRmdkvtTLddYlIHg9fFwBCqDpF6Ai5rCvdM++rNI/Zr1tESrLR85ef6uo4iVBbnknXlVtqJdJ1UH9uAlMk0CUiqUAoVRbs15viHdA9p3WLSCqASNJrU45dcp4zehIJj8umUSJCXbMuCmse0rHeNUB/bgJjIZCLCNnoH8oGRulv6r1RiptQSCfNjuWqrXccReGuHUMqDfHlMDS9Ik+J0lNN3WDTaqOuQGMuQk3tNQgDpgkgOSZ1UbNFwmkRWe+N6LONk8BFw7Z8+4itx3RFf4YrS3pZ9HMgvJcfbWMNoXFOzaPqiUCRaaflXHnEFR0DaXmRV0iv+2paAV+4phw7Wef4Q7hHicSq1tbCBMsLD0JESRNK9JBikfo0EdKOefZccV/X1QEbRcZ6T9fPhzGBQQnkiYaciJpCv5F0SUlPiLInZP7ydkimerWp2qCD88FHQSCvnVXa0ZUabFTt4I0f0SBZD0FgI6n1QEk/jId83UqAc7L6PSj22VfSRyVRkp4Mcl5oqOFFEca6oChqZrEKIWSd7WRJJMqyqibJkBUO4sLf67arSKJNLmazjdXOGsXV9yBMoIAAb5qPjB8VpgsqVvOm9j1JqQQ4fXaWKbxXcHrvsgUEkvmoNLgima+6ptaWy4GQUPmDagpEYWF6pXgiYoIIcX+2bbz43Cm+z33MxqqFgrgf6eggW1JJeC1VfLsA+nMTGDuB1O2zrnzE2Mfu8fVHIL1MsEqtOrL7O8t4jpQqNCzVT6RtGjSQotl8ahqPvQ1lY9lE+8Y+msaPB6NHMncCuUO16nSfO5u5zT/vbMjKgN7nU93yzolUssZPmPwpfzPnRRzr2PLoeIh9jU6FOGlox0gSVmoaj80PMXF9rKneWvObV7IL4xjl5amur8P8qMxzxjwvWZXyjGuKmJoKmeS4x7l/N0lHNk1sERFhKYeDB5swy5vckZOaxvNDo6fwN6ZC0vOYPYEUb19Xanv2cGYIgJBvcoVYlRJ+S/vbqb0040chsgufIJWAU7Ri7eVeRETa7pc8fM1x9DP8ZU10ynkRURpTkRX8eZtsJ3q1y6d1VUkHhMOa1t5EWuHspm/HtgoKz3DKqNBql/LxRJPhuMfK1Nq9sy8RAX+KXDg4zF5nlF8T72kCoySQN1VLA3TxxVFeqrUPirf1W0avdR68hPM29eVY++CWOGEqMURNOFodEDZ8QskLU58ikkoPl8ZQLzFPf8UETMAETGBMBIYQEduOx3SFPRYTMAETGJDAoiJC5iUOJSK0UuIKXntCwCiRjX2QJBg+P1VS7ithGtWkmrx9Lp+77eiAF9uHNgETMIG+CSwiIoTyEpVA+1D+9xBJP430eboXkj9CHHW1yukOYTfEy0/MfZ4+z/n/JTInmRuRDk/rcuT0DcHHMwETMAETWI5AqYgQwvtmSdeUtEfkieRJhXePMhGMoq51aF6RslpxMn3XArLcNfS3TMAETGBjBEpE5AIR6vWgSLIh5KuaucjqBIc6oW9NIb5EMlDMizC4lEuSYq4pQkYs8ukbI+ETm4AJmIAJLEygRETSSoE4eSqYHl9zlrxQV1NpCPwpmLSIQSZMkmJ2xCHjByGpxQKy8OXzF0zABExgswS6RCR/8Nc1PkmjT1m9Xa0YERhq4B8bcdWfjnr39G7wZgImYAImsGUEukQkryfflmSVqpx25YiQEUnRMmqxUIeLqK5tzfDcskvt4ZqACZhA/wS6RCRlMXLmW9R0z+LveZVThAHHel2DFM5F5zgc6PSqbmrZ2P8sfUQTMAETMIFBCHSJSKon39Y0JTnV6ZbVVGOfkgD4U54YfhEivHDYu1jjIJfVBzUBEzCB9RDoEpHk62gSkbw0clPNefJEHhydtR4RjvTUgL5t5bIeAj6LCZiACZjA0gS6RCRFXZ3S0EuBVo0U6toxmlThMM83BARfCiWTEZCj4sO0wqGZFcmHXS0el56gv2gCJmACJjAcgS4RyR3hu0k6PBsKvpCXhAggFO+q+EKSgBC+S9nkfbLP8YnQ2Opm0deafr91fpThZu4jm4AJmIAJrEygS0Q4wU5R4oR6+S+URL4IfhD8G4jAsyS9oRJllQsIYvPiEJGUpEjrRUqlPF3SyWHqcmvdlS+nD2ACJmAC6yVQIiKM6IphkiLxkFXElyWR40Gnw5NqVhF1fRiqSYjJ35JmnNfUWi8Fn80ETMAETGApAqUistTB/SUTMAETMIFpE7CITPv6enYmYAImMCgBi8igeH1wEzABE5g2AYvItK+vZ2cCJmACgxKwiAyK1wc3ARMwgWkTsIhM+/p6diZgAiYwKAGLyKB4fXATMAETmDYBi8i0r69nZwImYAKDErCIDIrXBzcBEzCBaRP4/3wb+Iz4QaxqAAAAAElFTkSuQmCC" width="200.5" height="115" /></span></div><div class = "S4"><span class = "S2">Further we define a vector of unknowns </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALIAAABACAYAAAC+0C16AAAKYklEQVR4Xu2dZcwlSxGGn4u7uwQJrsECwRM0Ibg7BIK7a3B3d3cNGtyd4BIgkCAJFiy4S55N197eYWa6Z87s+WbP15PcH3e/me7q6rerq96q7nMU7Wka2AENHLUDY2hDaBqgAbmBYCc00IC8E9PYBtGA3DCwExpoQN6JaWyDaEBuGNgJDTQg78Q0tkE0IDcM7IQGGpB3YhrbIBqQGwZ2QgMNyDsxjW0QU4B8JuCWwHOBPzbVNQ2sSQNTgHxC4MlJ+AcAf17TQJos+1sDU4Csps4LvAL4PPDQBub9DZ41jX4qkJX9qsBbgScATwf+vqYBNVn2pwbmAPlYwH2BJwIPAp4G/Gt/qq+Nei0aEMj/3UAYg757Jndjg2bap00Dm2lgCSA/EHjBZmK0r5sGNtNAcy0201/7eiUamAPkCPb0jaXj/rqSsTQx9rEGpgK50W/7GCxrHvoUILeEyJpncp/LNgXIpqhvCzwP+O0+11sb/so0MAXIKxO9idM0cLQGGpAbGnZCAw3IOzGNbRANyA0DO6GBBuSdmMadGYR4tKryMRUjugXwunivAblCY+2VrWngpMBLgW8DTwH+AjwCuAJwc+BnwEVSbc/tgC83IG9tblpHEzRwbuB+gAc3fgcEsH8D3DtlkU+dLPbDgF83INdp94KpRPU7da+3tzoaODNwRuALM6sszwG8MbkQzxjTbnMt+rWjXq4LnAV4Tqu3nr1AjwHcDDg28JoZerwK8MHkWnxyLpCdxNcDl+408PxUWP+37N+vBbyz857+y02AH8xWw958KIhvDGhNtALt0MBm86A+xcHxZoBZd0LfuIijkkU+PfAs4IZpLEaUTm634s12rgS8GvAbQX0P4Ceb6WBPvr4McPd0YOCXeyLB7nV6fOBxwHuAj1YO7wQJe8cF7lo6uV8C8jGTY/1g4LNpm/jxgCC5Bb8+8PZKgdf0moGErsSLJyh8TfKvWRYDuScB9wJ+VCFo4Ol9aRGMnmQqATlWxe2BPpcil+c8wJuB/6St+XsVwq7tFSmdS2QR8trkO5LlEWu6CicDHgX8uzAYd0ZBLF/8rtLAS0A+Q4oYrwjcCXjRSIPhmHvCWuD/vtT5yv6uS6Rr5GGBD61Mtl0R50LpWNwdElc8Nq47JpfiRsB3SwooAflSKWo8cUXk6GrzegCvCXh4xYorybbtvxuwRnAh8d6e5TUgjiwD/lqKtYbcheOkU/rnSrdbySmPPiUg3wp4VYV/nLsgRphvKnW8sr+H4gwsvOogZ2S6ohpFvzb7x49nWaf83dDd+9NkHCTvNxx7l036cIpdbF+Ld59EHeqHPj7dQbIU8yKddklAF+zKiZ78anIp1cm1U+ZNgzB0rZrx1kULu/bZgDcA30xBtxm+2UCOyVUoOcCxyDFcEB36a+apw5IAA3+3HRfDhSd8r9sT2Z8Jnx14NeTXFxsl3uHAL2EJGBe48vXFDnmQbHve//GPqUKNvC8LYD2Ci872zXLJLPlv0p2ORx0KJu/r61Kjc0TRmj4kjeUtwLMBE0XSlI8FrpEaLe3I7ny+P+QymAR5JaCPrPwvS+MbvaJtzCKfPAFYAXUVpE+GtoJwQeSOIyc+R1nxzbaBLDD17U2PFgML4JQpdrjaQOwQqdUbVMQWc/XknDwauA3wT0BZvJrhF8DpUs2Cc7fJAg/Z4pjbXYBH9hw6zvMIpR35YsC7gVsvGYuMATkm95xpyxib4NhGS8zG3Ek73N9dHvgEcFngMxWdxfZuCttT5d6Flz/B4Jx14O8VXYy+EruloHlm2qq9KCfnvSNm+UAyLtYrzHnEiMG7lKSW2CCs67NqPT8NfB9w8X5jpKMwUsZTBteLPGNAjlVWEi53QfTPSlvzIoIv3Ii7iFVWpUmIbgP4Q/5xMDgl7n3uMPLd8uvATdM2n7cXvrx/N1M5lw51Mer/atjUjynj7hNYCX/9VyMDi/oJ3Z2acs0qHQ0BOa8LfW8hcsyVarndaE68Sqrtv+Sk33/ChIe1G/J/4++WJGopi8HKxCHnu6VUlv103b7YJTe1yAZ2tj8WtBrAGVjWxAPhlrnzHXYgB01ioFBy3mMbNZgp5sQnTti2Xp8CZAMtJ8wtto9bt6bAy2v0Jw2O1N/ST1hAq8q0xj/s6SB86FKgPiZbPtYhHORYKeUa7GurQM4TITrlY75MKHXJRMi2g70prkX4x1JEfQxNUEfSVPrPSydX3C11g/xvyALm4CoF6mNAznFwyImM7KPzJ9/Z6yL64oVu+zG3slKLLfIh1yIH0pi7kLsgQQVtcrtnDHrbQJ4S7EXqtI+hyQMjOdCqrNREc50zIkNGJvR39sQpf2RiH33z0BcISzNaBK9bMRQvDAHZEyAHjyrNlO/gZzVAHovkI63rqrwO8MVNBdqj76fQb7oUL0x+Y9f/jSvFtMZL7lC5WiJYMuvVZwFrWIZaNecGpQ8HF0/jdJeqpfmC4Vg0nhoCcihLzm9se7we8LbkE1rieaTeXn+qxJkbkZdYl/A9uxN3WuCpwFdSUYw/GnQ4UvXBiAyxEcEyaI11B2rLJvvAnQPZrF1OwTpecwsnSkFyLWMlg2JgvWg8NQRkCXAnQrLdbUN/rJvmvECySirAq7SO5ONAkYk7RUV2MIAs1SQz8POUgNDfkyFw69diD01sfF9ig4asZjAifbSovrGlknce+TWBKf3HAr96woNuhLXoLhJdA7NuxkjuUjUWNvTsTn63JX+DZoxHjm3yfGnbMCXrpJ0kuREKb22y22uxOql2L9vD9zwYYKZMK9bHAoRosQv5/9YZmGjQOpnxsuxQqyxjoSFwl/pDZ0wBpDm0WF7TYrMvTwGTlYa6R9b6CijZEhdTX43FlP5zNyXG+6e0cJ13jZd+rjUqNRY2FoZul4tgsadUNGShuTyi24ppaB+J9c+loo5P7dD9yPLhKlfyf+xQgJSU3K2WUQsosa87YnCXR/nqqu+41xQgdSc6GBPnRet4uVTjoAvgvGjl5Xw1LENB99T+u+PVlXSXtigpAt931JziSKeI7N+dvqa4vhroJSBXN7QjL7pg5WXdmoulgzPGXEOdjTUbwJE/9lDnWAatr51N+++2GW5ODcWn1bbW+1sDCZwZ6jz6kwbkQ9VnbKCPKfe7RMVYd3JOA7wklT/2pZVLkxmMSU0Gra+tTfvP28y56m4g2Ne3FKcul+chpy7Akl4OlCS251ANWCRlIGNkbUC11BM/62ZgrGsyNZWf17TUZNC6cm/af7e9YLaUq8SXG0N4iNn44UtLKTRvpwG5X6vSjgZ1/pbgUr+7rV9r8GcQNic49nuvZ7CgfSjLNoaRTfvvth00YClo1cc2CNUd+tjMi1qK2G9AHlaRpxg8DW7dxBpu6I86Xqkr6VB3jb36IaI8oytz4Q5hGacHj/NHEOtKmCizTHaJrG/vjDUgj691C1w83rO4T1c0Mf//QveIVckSzuii+pM8TR4f9bk70m0GeT+tbnnmiw3IMxXXPluXBhqQ1zUfTZqZGmhAnqm49tm6NNCAvK75aNLM1EAD8kzFtc/WpYH/AbE/XV/gAhUdAAAAAElFTkSuQmCC" width="89" height="32" /></span><span class = "S2"> and write the system (10) in matrix form as</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="177" height="48" /></span></div><div class = "S4"><span class = "S2">where</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">A = [ 1 0 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">      0 0 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">      0 0 0 ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">  </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">B = [ 0 0 1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">      1 0 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">      0 1 0 ];</span></div></div></div><div class = "S12"><span class = "S2">The characteristics</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">determinant = simplify( det( A'*dx - B'*dt ) )</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S11">Dt = solve( determinant, dt )</span></div></div></div><div class = "S12"><span class = "S2">are again typical for </span><span class = "S16">parabolic</span><span class = "S2"> equations, representing infinite speed of information spreading.</span></div><div class = "S4"><span class = "S2"></span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">Additional reading</span></h1><div class = "S4"><a href = "https://www.springer.com/de/book/9783540678533"><span class = "S0">Wesseling, P. (2001) 'Classification of partial differential equations' In Principles of Computational Fluid Dynamics, Vol. 29 of Springer Series in Computational Mathematics, Springer, Berlin.</span></a></div></div></div>
<!-- 
##### SOURCE BEGIN #####
%% Example 1.1: 2D compressible irrotational flow over a thin profile
% 
% 
% The leading order correction of the velocity field due to the presence 
% of the profile $\vec{u}_1=(u_1,v_1)$ is governed by
% 
% $$(1-M_{\infty}^2)\frac{\partial u_1}{\partial x} + \frac{\partial v_1}{\partial 
% y} = 0 \quad \text{(3a)}$$
% 
% $$\frac{\partial v_1}{\partial x} - \frac{\partial u_1}{\partial y} = 0 
% \quad \text{(3b)}$$
% 
% where $M_{\infty}$ is the Mach number.
%% 
%% a) Determine the type of the system (3)
% Let us re-write the system using matrices:
% 
% $$\mathbf{A} \frac{\partial}{\partial x} \left( \begin{array}{c}u_1 \\ 
% v_1\end{array} \right)+ \mathbf{B} \frac{\partial}{\partial y} \left( \begin{array}{c}u_1 
% \\ v_1\end{array} \right) = 0$$

syms M
assume(M,'real'); assumeAlso(M>0);

A = [ 1-M^2,  0
          0,  1  ];
B = [     0,  1
         -1,  0  ];     
%% 
% The characteristics can be computed by

syms dx dy
determinant = simplify( det( A'*dy - B'*dx ) )
Dx = simplify( solve( determinant, dx ) )
%% 
% Therefore, $M>1$ would lead to two real characteristics and the system 
% would thus be hyperbolic. On the other hand, no real characteristics can be 
% found for $M<1$ and the flow would than be elliptic. The critical case $M=1$ 
% is parabolic. This result is confirmed by experimental observation that supersonic 
% flows contain shock waves, while subsonic flows are smooth.
%% 
%% b) Convert (3) into a second-order PDE using velocity potential
% Substituting the velocity potential $u_1 = \partial \phi_1 / \partial x, \ 
% v_1 = \partial \phi_1 / \partial y$, the equation (3b) is identically satisfied
% 
% $$\frac{ \partial^2 \phi_1 }{ \partial x \partial y} - \frac{ \partial^2 
% \phi_1 }{ \partial x \partial y} = 0$$
% 
% such that only equation (3a) remains to be solved. After substitution:
% 
% $$(1-M_{\infty}^2) \frac{\partial^2 \phi_1}{\partial x^2} + \frac{\partial^2 
% \phi_1}{\partial y^2} = 0 \quad \text{(4)}$$
% 
% We can classify second-order PDEs based on the coefficients multiplying 
% the highest derivatives. The generic form of second order PDE reads
% 
% $$\sum\limits_{i, j=1}^{d}\frac{\partial}{\partial x_i} \left( a_{i, j} 
% \frac{\partial \phi}{\partial x_j} \right) + \sum\limits_{i=1}^d b_i \frac{\partial 
% \phi}{\partial x_i} + c \phi = f$$ 
% 
% where in our case 

a = [ 1-M^2,  0
          0,  1  ];
b = [     0
          0      ];      
%% 
% The eigenvalues of $a$

eig(a)
%% 
% have opposite sign if $M>1$ and (4) turns into a wave equation. On the 
% other hand, the eigenvalues have the same sign if $M<1$ and (4) can be transformed 
% to Poisson equation by stretching coordinates. The type of the problem is therefore 
% conserved.
% 
% 
%% Example 1.2 a): Find the characteristics if they exist
% We know by now that characteristics exist for $M \geq 1$. The characteristics 
% of a 2nd order PDE with 2 independent variables can be computed by solving
% 
% $$a_{11} \left( \frac{d y}{d x} \right)^2 - (a_{12}+a_{21}) \frac{d y}{d 
% x} + a_{22} = 0$$ 
% 
% for $dy/dx$. In our case
% 
% $$(1-M_{\infty}^2) \left( \frac{dy}{dx} \right)^2 +1 = 0$$
% 
% $$\frac{dy}{dx} = \pm  \frac{1}{\sqrt{M_{\infty}^2-1}}$$
% 
% $$\xi = x + \sqrt{M_{\infty}^2-1} y$$
% 
% $$\eta = x - \sqrt{M_{\infty}^2-1} y$$
% 
% where $\xi =$ const. and $\eta =$const. defines the characteristics. We 
% can then find the solution $\phi_1 (x,y)$ as a function of $\xi(x,y)$ and $\eta(x,y)$, 
% by converting the differentials
% 
% $$\frac{\partial}{\partial x} = \frac{\partial}{\partial \xi}  + \frac{\partial}{\partial 
% \eta}\quad \text{ and } \quad \frac{\partial}{\partial y} = c \frac{\partial}{\partial 
% \xi} - c \frac{\partial}{\partial \eta}$$
% 
% This brings the equation (4) to the normal form
% 
% $$\frac{\partial^2 \phi}{\partial \xi \partial \eta} = 0$$
% 
% with solution of the form 
% 
% $$\phi = F(\eta) + G(\xi) \quad \text{(9)}$$
% 
% $F(\eta)$ and $G(\xi)$ can be determined by substituting the Ansatz (9) 
% to boundary conditions. As further simplification, we use educated guess and 
% say that shock waves should not travel upstream of the profile, therefore
% 
% $$\phi_1(x,y>0) = F(x-c y) \quad \text{(10a)}$$
% 
% $$\phi_1(x,y<0) = G(x+cy) \quad \text{(10b)}$$
% 
% where $c = \sqrt{M_{\infty}^2-1}$. 
% 
% 
% 
% Assume a parabolic profile 
%%
syms x y c epsilon
assume(x      ,'real')
assume(y      ,'real')
assume(c      ,'real'); assumeAlso(c      >0)
assume(epsilon,'real'); assumeAlso(epsilon>0) 

p   = 1-x^2;
y_p = epsilon*p;
p_x = diff(p,x)
%% 
% The velocity on the profile surface must be tangential to the profile 
% (no penetration boundary condition):
% 
% $$\phi_{1,y}(x,0^{\pm}) = h'(x) = \mp 2x \quad \text{(11)}$$
% 
% Subsitution of (10) to (11) gives
% 
% $$F'(-1<x<1) = G'(-1<x<1) = \frac{2x}{c}$$
% 
% which after integration gives 
% 
% $$F(-1<x<1) = G(-1<x<1) = \frac{x^2}{c} + a$$
% 
% where $a$ remains an undetermined integration constant. Before and after 
% the profile we have a symmetry plane at $y=0$ (no-penetration in case of irrotational 
% flow): 
% 
% $$\phi_{1,y}(x<-1,y=0) = \phi_{1,y}(x>1,y=0) = 0$$
% 
% $$-cF'(x<-1) = -cF'(x>1) = 0$$
% 
% which leads to
% 
% $$F(x<-1) = b, \ F(x>1) = d$$
% 
% where $b$ and $d$ are integration constants. Due to the hyperbolicity we 
% can assume that the incomming flow in front of the profile is undisturbed, 
% 
% $$b=0$$
% 
% Moreover, we want a continuous velocity potential:
% 
% $$F(-1) = b \rightarrow \frac{1}{c}+a = 0 \rightarrow a=-\frac{1}{c}$$
% 
% $$F(1)=d \rightarrow d=0$$

phi_0 = x;
xi = piecewise(y>=0,x-c*y,y<0,x+c*y)
phi_1 = piecewise(xi<=-1,0, xi>-1&xi<1,(xi^2-1)/c, xi>=1,0)
phi = phi_0 + epsilon*phi_1;
%% 
% 
%% b)
% Let's try to plug in some values
%%
c = 2;
epsilon = 0.1;

u = diff(phi,x)
v = diff(phi,y)
%% 
% and plot the solution

xmin=-2; xmax=2; ymin=-2; ymax=2; n=10;
figure(1); clf; hold on; axis([xmin xmax ymin ymax]);
fplot(subs(H),[-1 1]); fplot(-subs(H),[-1 1]);
fcontour(subs(phi),[xmin xmax ymin ymax]);
fcontour(subs(xi),'kREPLACE_WITH_DASH_DASH','LevelList',[-1 1]);
[x,y] = meshgrid(linspace(xmin,xmax,n),linspace(ymin,ymax,n));
quiver(x,y,subs(u),subs(v));
legend('upper surface','lower surface','velocity potential','characteristics','velocity field');
xlabel('x'); ylabel('y');
%% 
% 
%% 1.3: Time-dependent diffusion
% $$\frac{\partial \phi}{\partial t} - \alpha \left( \frac{\partial^2 \phi}{\partial 
% x^2} + \frac{\partial^2 \phi}{\partial y^2} \right) = 0\quad \quad (1)$$
%% a) Classification based on coefficients
% The generic form of second order PDE reads
% 
% $$\sum\limits_{i, j=1}^{d}\frac{\partial}{\partial x_i} \left( a_{i, j} 
% \frac{\partial \phi}{\partial x_j} \right) + \sum\limits_{i=1}^d b_i \frac{\partial 
% \phi}{\partial x_i} + c \phi = f\quad \quad (2)$$
% 
% Let us select $x_1 := x, x_2 := y, x_3 := t$. Then the matrix $a_{ij}$ 
% and the vector $b_i$ for our case are given by
%%
syms alpha
a = [ -alpha   0      0
       0      -alpha  0
       0       0      0  ];
b = [  0 
       0
       1  ];  
%% 
%  The eigenvalues of $a_{ij}$ 

eig(a)
%% 
% imply that the matrix is semi-definite, and the $rank(a_{i,j},b_i)$:

rank([a b])
%% 
% equals the number of independent variables. Thus we conclude that the 
% PDE is parabolic.
% 
% 
%% b) Transformation to system of first-order equations
% The original equation can be transformed into a system of first order equations
% 
% $$\begin{array}{rrlr}\frac{\partial \phi}{\partial t} & - \alpha \left( 
% \frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y} \right) &= 0 \quad 
% \quad \text{(3a)} \\\frac{\partial \phi}{\partial x} & & = P \quad \quad \text{(3b)} 
% \\ & \frac{\partial P}{\partial y} - \frac{\partial Q}{\partial x} &= 0\quad 
% \quad \text{(3c)}\end{array}$$
% 
% by introducing the auxiliary unknowns $P = \frac{\partial \phi}{\partial 
% x}, Q = \frac{\partial \phi}{\partial y}$ . In general we cannot say that the 
% system is equivalent to the original equation, because the transformation can 
% create spurious solutions. The solutions of (1) still solve (3), but not vice-versa. 
% Therefore, the type of the first order system can also differ from the original 
% equation. We will see that our example illustrates this problem. Let us write 
% the system (3) in matrix form
% 
% $$\mathbf{A} \frac{\partial \vec{U}}{\partial t} + \mathbf{B} \frac{\partial 
% \vec{U}}{\partial x} + \mathbf{C} \frac{\partial \vec{U}}{\partial y} = \vec{f}\left( 
% \vec{U} \right)$$
% 
% where $\vec{U} = \left( \phi , P , Q \right)^T$ and

syms alpha n_x n_y n_t

A = [  1    0     0
       0    0     0
       0    0     0      ] ;
   
B = [  0   -alpha 0
       1    0     0
       0    0    -1      ] ;
   
C = [  0    0    -alpha
       0    0     0
       0    1     0      ] ;
%% 
% We can analyze the system either with Fourier method, which analyzes whether 
% solutions can have the form of a plane wave, or with the method of characteristics. 
% Both methods lead to similar equations in the end. With the method of characteristics 
% the normals to characteristic surfaces are given by
% 
% $$\det \left( \mathbf{A}^t n_t + \mathbf{B}^t n_x + \mathbf{C}^t n_y \right) 
% \overset{!}{=} 0$$

determinant = simplify( det( A'*n_t + B'*n_x + C'*n_y ) )
N_x = solve( determinant , n_x )
%% 
% i.e. there is one real solution and two complex solutions. The real solution 
% $n_x =0$ is typical for parabolic equations, since it represents the infinite 
% speed of information spreading $\frac{d x}{d t}= \infty$ . The second component 
% of this normal vector $n_y =0$ would be obtained by replacing the equation (3b) 
% by
% 
% $$\frac{\partial \phi}{\partial y} = Q $$
% 
% The two complex solutions $n_x = \pm i n_y$ most likely manifest the spurious 
% solutions created by the non-equivalent transformation from (1) to (3). The 
% system (3) is thus _hybrid _since it does not fall into any category. If we 
% did not know the type of the original equation _a priori, _we would conclude 
% that the original equation is not hyperbolic because it has for sure less than 
% three real characteristics. One of the messages of this exercise is that second-order 
% PDEs should be preferentially analysed by method *a)*, unless it can be proved 
% that the transformation to first-order system is equivalent. Two common cases 
% where the transformation leads to equivalent first-order systems are considered 
% in the next example. For more details refer to Wesseling (2001).
% 
% 
%% 1.4 Steady 2D diffusion
% Neglecting the variation of $\phi$ in time (corresponding to a steady/equilibrium 
% state) leads to 
% 
% $$ \frac{\partial^2 \phi }{\partial x^2} + \frac{\partial^2 \phi}{\partial 
% y^2}= 0 \quad \quad \text{(7)}$$
% 
% The discriminant
% 
% $$D = B^2 - 4 A C = 0 - 4 \cdot 1 \cdot 1 = -4$$
% 
% implies the equation (7) is *elliptic.*
% 
% Using the same auxiliary unknowns as in 1.1b) we can eliminate $\phi$ from 
% the transformed system to obtain the Cauchy-Riemann system
% 
% $$\begin{array}{rlr}\frac{\partial P}{\partial x} + \frac{\partial Q}{\partial 
% y} &= 0 &\quad \quad \text{(8a)} \\\frac{\partial P}{\partial y} - \frac{\partial 
% Q}{\partial x} &= 0 &\quad \quad \text{(8b)}\end{array}$$
% 
% which is equivalent to the Laplace equation (7). Computation of characteristics
%%
A = [ 1  0
      0 -1 ];
   
B = [ 0  1
      1  0 ];

determinant = simplify( det( A'*dy - B'*dx ) )
Dx = solve(determinant, dx)
%% 
% does not reveal any real solutions, so the system is *elliptic *as well.
% 
% As we saw in 1.1), with more than two independent variables the transformation 
% of both elliptic and parabolic equations creates spurious solutions and the 
% resulting system is therefore no longer equivalent. Thus it is very often advantageous 
% to analyze the type of an equaiton or a system of equations with several independent 
% variables on sub-spaces of only two independent variables.
% 
% 
%% 1.5 Korteweg-de Vries equation
% $$\frac{\partial u}{\partial t} - 6u \frac{\partial u}{\partial x} + \frac{\partial^3 
% u}{\partial x^3} = 0\quad \quad \text{(9)}$$
% 
% We introduce the auxiliary unknowns $p = \frac{\partial u}{\partial x}, 
% q = \frac{\partial p}{\partial x}$ such that we can form a system
% 
% $$\begin{array}{rrrlr}\frac{\partial u}{\partial t} & & +\frac{\partial 
% q}{\partial x} &= 6 u p \quad \quad & \text{(10a)} \\\frac{\partial u}{\partial 
% x} & & & = p \quad \quad & \text{(10b)} \\\frac{\partial p}{\partial x} & & 
% &= q \quad \quad & \text{(10c)}\end{array}$$
% 
% Further we define a vector of unknowns $\vec{U} = (u, p, q)^T$ and write 
% the system (10) in matrix form as
% 
% $$\mathbf{A} \frac{\partial \vec{U}}{\partial t} + \mathbf{B} \frac{\partial 
% \vec{U}}{\partial x} =  \mathbf{C} \vec{U}+\vec{f}\left( \vec{U} \right)$$
% 
% where
%%
A = [ 1 0 0
      0 0 0
      0 0 0 ];
  
B = [ 0 0 1
      1 0 0
      0 1 0 ];
%% 
% The characteristics

determinant = simplify( det( A'*dx - B'*dt ) )
Dt = solve( determinant, dt )
%% 
% are again typical for *parabolic* equations, representing infinite speed 
% of information spreading.
% 
% 
%% Additional reading
% <https://www.springer.com/de/book/9783540678533 Wesseling, P. (2001) 'Classification 
% of partial differential equations' In Principles of Computational Fluid Dynamics, 
% Vol. 29 of Springer Series in Computational Mathematics, Springer, Berlin.>
##### SOURCE END #####
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