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</style></head><body><div class = "content"><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">1.1) Time dependent diffusion equation</span></h1><div class = "S3"><span style="vertical-align:-18px"><img 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" width="211.5" height="41" /></span></div><h2 class = "S4"><span class = "S2">a) Classification based on coefficients</span></h2><div class = "S5"><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="302" height="47" /></span></div><div class = "S5"><span class = "S2">Let us select </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="152.5" height="21" /></span><span class = "S2">. Then the matrix </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="17.5" 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="16" 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 = "S10">a = [ -alpha   0      0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0      -alpha  0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0       0      0  ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">b = [  0 </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       1  ];  </span></div></div></div><div class = "S11"><span class = "S2"> The eigenvalues of </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="17.5" height="20" /></span><span class = "S2"> </span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">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="86C6C6DC" data-testid="output_0" data-width="1141" style="width: 1171px; 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 usesymbolfont Linux 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="48.5" height="60" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S11"><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="90" height="21" /></span><span class = "S2">:</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">rank([a b])</span></div><div class="outputParagraph" style="white-space: normal; font-style: normal; color: rgb(64, 64, 64); font-size: 14px;"><div class="inlineElement embeddedOutputsVariableElement" uid="04A43CCF" data-testid="output_1" style="width: 1171px; white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;"><div class="variableElement" style="white-space: pre-wrap; font-style: normal; color: rgb(64, 64, 64); font-size: 12px;">ans = 3</div></div></div></div></div><div class = "S11"><span class = "S2">equals the number of independent variables. Thus we conclude that the PDE is parabolic.</span></div><div class = "S5"><span class = "S2"></span></div><h2 class = "S4"><span class = "S2">b) Transformation to system of first-order equations</span></h2><div class = "S5"><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 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/7yKnq+vImLSvCuMOYyyjKaU3JLr1HC2clVYCGc60u1KIh/sPC4d1yPScq9IytO9ifgS1YjYOOg9nHbQmUKzBif0Fw+XhpjexYYVoYu0F5+smx2rD/z2ncwezVCmx2xi/fcB+eD507mctTOiZVnYWEl2yTYKe+LWaU3tOXC443ZpJh+M/QOe1bvUGEW3l8W9yIZxqe9+0Nu4MPexeGuzvPTqfa46nnethVekCe1QdRld4KGbcdddT6dJFT2W4M644XnrCKpdqKdqtRRJvAUGfGqCfnddbgx1QdaTI+Rs3HOfcw9xv3CTD2ixU8ywzYW0bDMQO87lG+7EIHq7sJc6R7YxQW3HKPzvLp/Fs4uZRfv+XA+LL1hlwsdNfYliKoVshMemWF50b6ueQzj2qh1r9I4U3w8v+Eivy3B+zHc+y7mYDMm5skKlpOxizWAYWQjRpTDccNPCT0gOUxrO94Sm0VCz1BezpNMM3dOkrp6FcLKsp45im8XAPf6r3F5wy7GPqYx4OlBcmeJaXKn2IETD8aH2h+kBBUKkbUgzskKWyQyLCUMESUFx15js69nQvHZQHCPd0q8fV1rF+P2LiTeA+5knS64l3dtHQ+L4Vd+9Lu4sSMZoy/cpjNVfjOcphIHCyo5x1jo+JFZl5TgYNrScMC6ta1Y02zwxLGVQn3UAtezkgi/W/skR8rm5wV0ngQwSV/WUs9XDHJOLsHQxSrzvDfKnryni1J8YlJS37l87Mwuo3iBJIho5WPHLdDuhWJV2YnYlXcXiwcuE08SiRiFQvBlnJbDHnnnXOd4aopPmreAu+znRWIzhDN1G7HASJghw1KhbcY8hXNf2EIo5irxbllGH0u4e5qUWXHPn7NYe7SZI5twI/OQCF+9TouxUlZyOOgUySasvkVrWldSwlxyR9TiDYXblbvUM1tGpDI8Z1gL3hMqFz7fi1J8iKylWS/LBD3ll9DuiZITc7CDUSA97FxO0UlO8aDFgYas/GMu0ykchgXXfOh2Qucop6b4PCOLgziKOPeU7KKJrEQl7x859TKTdd5rNamdE1iCxngBHY41DBf4uxDEOdO7UVIKzckqj9PUM4G3Mp6hKCtQA8iTtUy64pvq99nPk6RC6fGQ8WKsKlMYEjkoZrdmLpSLUHwWffE97BaXNf6gdEMJB1HjIqV3LP6mRkbcj8sXHit3Jm2QYRsc5QiSjM5RTlHx9efE9c3Fg+3iqi1L1vfHEzBeQNZ9tsMkj1Uuv3XHnns8d/zUez/3fNnew0zhOedJ5uk9JeUPyKRdJFhHhjkKPDEU57mK5gL3bDe/Sf9TSXI24XAVH5RYwqPlediYKxthkU+JzYrSCZzNi/JGhol14vk6/qwSLlHzEkqgCBfKRSi+bq1s2kpn1c0e+vdh7EAyA7flFNmwmJTArzoj7l4PxyI4p8DTgmlhIJvwdB4ao11d/5QV364wmBqHe7Pvsu2mO1HBPq85HnvI47rJdaf4e1eNw2KzsSarFJ8FeVi4vgnt36r5nNLvw9Zx+JW79bfNPVj7vHs2QRJmeCLGbc3mjm9z2MlM5pZwiVl2ZhnPe2F280UoPjfPGhL05Pu9bDLsHD/sND++z97KhukO93VaLw0VH+aUfWYIHvPzKcU3/XSGm69DKb5DvDe9xMe1V7k6h64wx7NUzpnBpbezgoWSg94SbtvnOPQ+UHoyNqcUEFez0JfMTkkx4uGstSmRzCepb5VIfLNGEFZlJ9y/0nkXofhWTfaif6ecUNtsKh5Wp2njrlQ4290tah4Xua2UIfRMIy+EAO7cNjTDQDT2lt4EeNN7OObzFCMvynD1YYgVs6wXxRFk7q3bsumY8Zgzt+FiIzuvx/vmnHvKx4iZq0Ml6yS3IGAQ8ztnGSq+WUXfa4DlG7QZIxKvnjI6l0UoeaXH4RSfS7RhsfWsd3kTPRESM485rhJJhb0sQvJSJ28vxddKAVAYbSp2FD4cok6lUyR5cBagRTL0qfOHr1PMLC7Yi0sv+45+aL1s8owkUqFXOicZegS8gz1b77JjgARDchhZFdscvlezipwvOXjDgv5l/Tk3gUGT5t7SbExbxkiAf+cblv3Z+7AOrzV0dc5VfBu7OucWC24CxtxzTskKvd+AyFuCC764KbH7kJUkuWeTdj5igb3PGtdAb2A6F1PUczK3jkFsAMxnE9mVq/MY3vNlG6R18Rm2k7KgDEmaN8H5VM7ZtID9e1pS0anc5z7mKbHFt0jW6S4yZy7DTf64VMIGpXuseG3Q+U3JJopP+QRLkYuzZ/tODj5WMsewIJyS4pOmjhGCLGNUGQaSl7lDF71U6OIUPpNN3BKl+K6I7DG857tUfMMCdpukzhgzZ5Ha1THcVxTRpiIVnkJaR5RuaHVG1qEswxMsNn/OIq7XiTDmbEZRgtlQWedWydCaZM11JhfnyW3o2b/LklbWVXyMi95yindMKGmhnJKSWQX2IX7v/QVdexH/n/icYvWefeaB9gfEJYewe1Vm5/ChLuqTeIj7v+hr7sriu+h57/t6vbWX68BoV10f1pn3IbI6i6R6nSd0xWOHmcBzKNxYU7Is33IGjVhvVO6K49ptdX69wcGywnmkD71l1xxXp4bnvdaPQaJrRym+zd+PpWcy2ZnuZMoSw+bCnBd4t1sSqxNreHpjjtDCRgrwnOwygVqZaVhg7rGn+zn2YUvxTT+h3qRYshRXzzFbtLt+x6ot0WaIyqpUcsAlKN9A3sEy6W5EtcjLujMYpzcxEHND4DDMrsQN2gk4kHrI+pwiEhgqyDmKb+j1EHLqbfEm76ksvs1emn6W7MOuhMalDIK4Ei24VdTgoW3zoNXL3CYJd4AHPpdzUtG7os9lscTt7ub4zy7FN/2MeqxZw+ee5Xj8T3M3Mxw3opXVqqdkF3R/vj+WCn5IyTBzNpq7md1xj9IZtRTyq4NcxmQzjJ9hGxpnarpTiVXyD2RW2nwpQei9EjsSykieNaDxk4Ft7Ry2iep9RxkOZI7iG67FMsOXdv0pxbfdi+ljUpqgaBIPIPeBlFo1KQpydSTGMI4eCKuA3xTOeshcn/zQcws8e/dzL5YEl3OUUnzTT12sRsyGS12bpXMT/SXRWwkdYAJhkYhzWgDF4JXB6EPJWulhhnPDaOp+hy2EVmUDW8dklPeQjcxMlqJuCkpDlIip2SZcojb6i2oDWXkUJ8YXogRMyAfzDg+Y2K1yB9cjEvu6lagbx9TGhfcMO5JNjt6BS2WZ4vMbF51JKA7FNMKH6gWqJo7/C6sYno+OT9qOyW5GgoEdB6tOvUx3PSHq7k1kxWUox7nSFzcu054KPPfc8XGn+mz3pfi4fXz46opcA8Xe7zRFcgpuQwrP/B89SLba9N045fNsNPHgCifYfFpIfS8yqSnDU3iWF4m/dYAXyjo/p4GABCYeLOUzuijY+COpZg1ym6Igox8ovM66suh+PB9dFCg3BNO+QUpU5wyJSvInpsawiRmTX+PydB9kVrnXIsXn73gkFQsTlfcC5gq21bBJhcXCUi/SK/GxC7LbsMNU3K4gkyU3ZiwQo7PLUmfV2wzNfdF1qVcTsy2zfD3bKyIucYhrrLsIWQwWTAqQe1m8oNPFzX1WF30ccmaL0Lhm6qLnUdc7PQRYR1zA1i0KkLv81KRn17MSbX5WyjKLT1BS7OCRre6i95YTTOaXZXpyryzzC/Mb0+Jkk/q1lTdwRgfIGuVuIHzorJJNZRfPdtNrH+N5sLUhkd0mFdo77d2Vei3ILoVbUe4xCjcfN7pv+ZxbVh3jszmVOX1jki9rjD+YVk4pBso4E6uUGc/7tqxDx/88j01jfNyfYk7SUbFwL5JhseLK5oCn8pYcaJ4skh6w1cOq1y/tejpzn+2ur3us4+m2YQMofuQDOzYZMpJ4R05xx35smJ7bfOgBvUTlImierJfoKYSzZIj6JmWN0jVz8yX+e5e4qYgn6KckmC7GMCXDYkWBT8qyZHMEOinvvmv55jzbze/itM4Ue+CWlqUrdrsqdnHRd9dr+KSOC0WUFAKbIsDqu29rATQsOt90vH2ex7UvKYbukcDUmwzPuuY2iq/TJPEP91q28UV7Qoa/n3v/q1kPZMVB+vBJ156T3rvN9eY8223GP7VztZOyEChdUUd5TNJ5Eb0bejWWFALbIIAlSuLKsTe7FopgTD1mk5vdRvFJ6FD/IZVVrUyvsh/Og+kJxHOsL9rkeaw6RyovWihJF5gK9iVznu2+rn2M43Z3oh0md+LCPl8HmLwsOHyHi8h+DzClumQhcNwIbKP43JnUfZlAQ5JTHaWl8K8Sbs9e97Hq2Pr9lQh0miHZtD3tfl/YTD3bYXsk1xUHUFS/qBWTxAv1Oo6Rbr+0qHRfN7KDcdUbdRowGznYTAmLa1jYqwQIM8ZUAhjC8qF7Ri8x7pt1REYqFyc3LFagYeH2OuPUsYXAWSGwreKbcr3JLOOOU/MhW44odFTjMRTJGQKpJfMRYInJ5hTL2YSsev6Vkqlnq2RDKyZ1M33Tsojnz1yVxHCDa57b2yqtM4djOda9UPLifTZ2i8iU3SdWC5lx6jqJzYqawLHYDMgWRfGkaPeJg+9l7n2rWXIeBXr1uSfVcYXAuSOwreJTqIiEVEdwH/1Qbp8E+zaRKn7sPuNTeRfE95SUzO1KvOl9LXu2/OusN3WJUp8lfahdHIo6T8XEnj0leupCubDSUCOtavE07IZxxxWlEAqrKUtjLmrAuwi73vVjVWeCU8e+5l8I7BSBOYrPMQKeXClcN4qveyNWdWWsOq4fLqCh2BVb+IgFA11XyfYI3DjJTzTLD67bxJs2fbbuQpLH3drtjJNtFNtbxFmli2iLtkdi9yOw6LjuxU8pOvGzXtPUM2op9N5kc9EM8EFqkkpWMcUjMWcVzmKcGF1QqyrfprTun949HDViIXA5EVil+FA4+XC5troolrWjtdv8uSRqyrgx8a8NhXsHtRaFZ4Eu2Q0C4jmKNBWxcyl7BpvINs/W9WTpsvrEsChf46EN0s0ZFZtSlgduMrEDncPqQtvkvrqIXfJcUGJdAT54Rk8yY2B/8X0tS+xC2IuJh8JlRUsWmysSWihmpRYICbbZAM29Zh1XCFwKBJYpPi4qxYHanAjs37a5rCgxjC1+F1cQkNeGAn9bFx80q/A12qLBSinZHQK90aNOD7faYNhtnu3wcsMuzo9rCu/xSSgHNUGnIqi+WKmER0OdpM2cDR/meCzxnTB3TtNO4+C17Zm3vhHJK2PpyUoIdiUOrSO9I8MmLtJ1rlPHFgKXDoFFis+Hyn1pN48KBp/buFxhyMpCQWK26MLS6wF9BZF9Ubl0AB7ohriVn9E2Fyw/PHtzZdtnO7yOrEJWn44TxDwoPhujU+FxHTLUs5657rn0u/hGuG37O7wqZtfPw4SBAYMsYn3prDDrcmzaWLJGWYnKK1Y1Mp77btRxhcBZILBI8Q27CCzKHuTa6unT412w2F7PfDtWqqdTf8AUDKb0ZVmGU/e47bMdj9lrC/2dCxZRN6LnUxDvv3e4NwOWaSluNha0fPhpyVwGIh6S3gyThT5lAfOUyOrU0kVblrmivY6MaLHebonOPbeOKwTOHoEpxSeGJC7XM/cUp0+RlmoyiMCajMlxZXOKjRAtJ1549kjvHoAe4+FS45KbY2Ht4tmO76SzvPS/L6Ow2z0K241I4fUyG+8yrsIpEbMUuySs2zm0ZWLeWuIQSo1yGwpL3UaBxUzhriObKsx1rlHHFgKXFoEpxWfH3lPT9ZlTtzUlD2gJDBZc7rNh1uavtQ9dsH6YLHBpgTzQjSmWVjTNPaeea5Xs4tkOr0Hhqsdk4VnIyaxGkKsmekG/90Qcl+OlUBYwJZpuYm+Zyl5eNFWbDO+/kg/4cAsPiX+/tCX/SBTjMZkrLESK75wbEs/Fqo4rBCYRmFJ8QxfmMm7CrtwsfDI7uyj2lakmIaDYWfb74ungLrNPPPW6M6y+bZ/t8G4kNkkEkb3I6nt6Iy1wjPgvDtdjl6ELc+GRkW4AACAASURBVFHHCwoLaYAkLyUcvom5ImbYC/2HlrDvDp0fS0+h+zq9GXsm9bVbl/G5c6njCoFCoCEwpfjQTMnItGNd1AXAB4svkugo3gvV/Ztr9Lnttwe1LrsdcIuITE9tJE4lDnTsL0uP2c1hctn22XYsJD1h42HNoCJj7fcuAY6hEP392EU5SC+uX0T5NbwvrtHZrU+SdHJrOEhk4SUhSicUrnOhGn+u9KahYoca5JYUAoXABggsSm7pxLc+VB/sWL6hpXkr8rVjHWYVDmM+t2nNPfv5Yn1qjhQJi02VbI8AJQTLl7f0+VUZnts8W7Nl+SiWZnFQbj3bVy3aswdUXafA1sMNT2nbjE3N1/dBibOmN3EtDpsHS0YSC3/tVu94jcZ4Mzf+bY4SccyZAu4Nnrd/g2qEQuDMEFik+Lh90JBNJU5QWngXLYDoysZ8m1q/P6HhKFmgJ8B8YhK1XuOavzODfC+3K3NWew4bklV9tLZ5ttzYnre6TNYHJToUVGpYXAj3qzq1Y5e7th5kU1aUcgRlCTwUeEq7J2PuPb1Jc5M6Xi0sYvFuBS7aVC4aG0uOsgcsLU+eO4E6rhAoBK6MwLICdmnqPlLBdx+cJBaLpoVPEbvf7z8BqkQXKeFqjexmJcg4nhLkQtXhe90FpJ7dagT0Zbtdw1dB9DLZ9NlK6Zety5LplFzD61CMMhlZJOQRSf6mlbYcq4XvPUWmjVhaeQilws0v8QU9Gaaim24Rs5QoJqmI2KD4fhSzSwzq1H+rnq4MUZmhQgoYcUoKgUJgCwRWUZYJyAvoX6tdAy+gmAiFyHJbJNxGCn4tgBZDtE1PbRbJWp1yt7i3czuVK0zcTQsdSS+rUu7Xfba92JoVRKEtEsqDW28oYsLPP+IH4juQ1SleLQ6q+4XkLFa0jMtt2il1UnG3/7I2/jq8nPpd4vOkJJVEVGz8iF+kmtppILBK8fW7sAPmphFXqA/veJ+tDYpF0n9czlN94Mazr2d7RUTE4K7aXJO74L/E9ILCrQtiB6QDc+XRLZbK2zJVXD93nDquECgEGgJzFV8BdjoIiKuppcPjKV2/5LAI9O7tZqEOUKxwSIm2bHZCDJSk2r2eRX3Yu6mrFwKXAIFSfJfgIU7cgmxL/Q8lUOBKLdkvAsoTxO3UtI7lFq3DCdczIuq5CsymBQE18ne8rCWFQCGwIwRK8e0IyCMcRpxPCr5klGoCvL8HJIatVx/eTEquC3epxDAKjIUneQbpwxzR1Fk29Cc3t/Wcc+qYQqAQmIlAKb6ZQNVhhcACBHSfV78oHihjU9mC2lZUchJldE5QyoPZpqQQKASOAIFSfEfwEGoKJ42AUgOlJMoTWHmSv9C4cWkqjVAfyCIsKQQKgSNBoBTfkTyImkYhUAgUAoXAxSBQiu9icK6rFAKFQCFQCBwJAqX4juRB1DQKgUKgECgELgaBUnwXg3NdpRAoBAqBQuBIECjFdyQPoqZRCBQChUAhcDEIlOK7GJzrKoVAIVAIFAJHgkApviN5EDWNQqAQKAQKgYtBoBTfxeBcVykECoFCoBA4EgRK8R3Jg6hpFAKFQCFQCFwMAqX4LgbnukohUAgUAoXAkSBQiu9IHkRNoxAoBAqBQuBiEFik+Pz9XZJ8UJJrNHb55zTuwX+/mKnVVQqBQqAQKAQKgd0jMKX4/O1Hk9y0XQ7rPMb5qyV5aZJ7Jvn2JP+1++nUiIVAIVAIFAKFwH4RWGTxvU2S+7WeYE9Nwsp7zSSfnuRbWn+3z0jyn/udXo1eCBQChUAhUAjsFoFNYnzcn7+Q5KGtyeZuZ1SjFQKFQCFQCBQCe0RgE8VnOo9OcvMk10/yq3ucXw1dCBQChUAhUAjsFIFNFd+NWqLLzyb5iJ3OqAYrBAqBQqAQKAT2iMCmiu9VkvxDktdL8o5JnrfHOdbQhUAhUAgUAoXAzhDYVPGZwLNaycMdWpbnnEm9RhKJMxSlbFEK9F2TXDvJnyR5WmWLzoGxjikECoFCoBDYFIFtFN/PJPnwJD+Q5DNXTODtktw7yccleUKSz0rib49Icr3Bub/Uyij+dtMbqvMKgUKgECgECoFlCGyj+H4wyacloaxusOAir57kzq3275+TfHyz6t44ye8luXqSVyR5tcH5P53kY+qxFQKFQCFQCBQC+0BgleLz+1sluU5jb/n1VsRuLj+e5BOay/PdJibn3O9Ocut2zgck+cN23A8n+dQkD0nyZUk+MskTB2OwBl+4jxuuMQuBQqAQKATOG4Fliu89kvxQi8F1lP41yVcn+eYkP5fkg5P8QZL3nICRpfeA9vevTHL/9v/fPMmfJ/mzJO+U5D/a37lAWYTk9q1O8LyfTt19IVAIFAKFwM4RWKT4PjbJjzW2FnRlt00ipvcWSTC2+J2b8i2T/GKSDx3N7B2SPDeJ8f86yTUb+4vD7pjkwUm+Nsm9Bud9UWOF8afvatfc+Q3XgIVAIVAIFALnjcCU4qPMZGy+QbPMPmyiXEHtHiozQkHebAQji/CL29++I8kXDH7/kSSfMlH8ztpj9RGsMKy+kkKgECgECoFCYKcITCm+b03yhe0qsjVlbY6FG/T32x+/prk/+zFXSfIXTXH620e3Yvf++4uapfj6SbhOu0iUkTBDuEkfuNM7rcEKgUKgECgECoHmihwC8apJXpJE1uUft+J0WZdjUY7wyPbHT0ry+MEB4n4yPbuwIF/c/sE9Kr43FRcUB/yGdpxkmq5Y60EVAoVAIVAIFAI7Q2Bs8b1tkhe00b8/yS0XXEnSCqtMayKKjbLscqskD2v/+KckVx0UpX9ya3n0vUk+bzR2rwt8RkuWqbZHO3vMNVAhUAgUArMRkJOhE48OPacgdMlvtxK5WfMdK76hC/MeSe6zYJRfS/KBSX6lZXYOD/ucJA9vf/ijlrnZf//GVr5wuyTfOThJ+cLz27/HFuSsG6mDCoFC4CwRGOYGrAJABrlku6cneVTLT8AgVfK/CFi/9VvVfECZ2ZS8TxJ8zTr1YN56syRqtv+xJTXicGbcCGuN5e0XUFxqfK7Z+SbCEFMWR1HfrbGCLR1nrPheq9XccXlKTtF7bywyNik0IhaoFm8oOjb8cvuDonVJMt16oyiBBbjfaceYA7epeOJjW6JMWXubPP46pxA4PwSwR9ksEx4l5VLkMUn+agCHtc3aZX1ClUh+sq03/3Z+sE3esUx7Bo+2czdJwmM3FNzMiEd4BsnftfprdJPwfefGzkV/vCzJl06UpQmj3b2dLyz23u3/b6P4XE8SJctPfbn3YGmv2Knklt9M8n6tBu8rJuARhxOPk8BCe49fGg1rafo3bee+dZI/TYKn047ASwfAXr9nsgrdn5nkQ5L8fb2EhUAhUAhsgIDSq77uWGCnqA9tup+c5Gpt/Acl+ZINrnXZTrlN88LxvL1vW6vH9whTFjP50STCWi8dHaQ2+ycaJaWfkJwMyUmGh3cPoL9to/icT6/YyHxUuw9exYUypfh6cgqzkxk7tL5M7ndbfZ8sTAwsU6LujwbuAClfeP9GV0axXrfRlH1Vq+UzptrA4Q7tsr1YdT+FQCGwPwR64pwrIMe41pJL8WYpuSIW7jdpFsr+ZnfcIzNOsGrJyOfC7KVq41l3xfc3jdFrmJU/PNZa/qT2B94/Bs2U7FLxGR/LGL3F+kR7if5yUhYVsN8lyde1MgXk0pQfhUjRKWL3e2dimRrYuM53HJH1ydr77CQ/n+Q3minN9cCdyvT99+N+N2p2hUAhcMQIIMDvloX/ZWkskr4J77+fe2u1TiEpQYS3b5EIW4nf+Y/Xb5G8bhJhLsKD90YLDty14nMZscXPbeE4rtfJsNkyyjK+cMktfedEm8q8pNCwtcwR8Txti1h42hG5Hr+xtkQ/1bI/lU2UFAKFQCGwDQL3TKKmmIxZocbj4g3GO9xFzOpc16FrtHvXKEBMrlvC2zyL1xm4QIXEWONTsg/Fd8NGp+l6NkPcrleSVSTVThA4FDDm2+1xuXVBcR1uTKYyEIBRUggUAoXArhB4XJJPbIPdNIl/LxKep+9rP3LXKbl6+a4mcmLjyOPoZQvv3nIttr0F7lJxVKK0TaOCOYpPfFFsDi0mbyDXq/wQjF4yN7lYV4nsUk3SnYslTDOEK8kcxbfqQnN+12hWfd64vGHOuXVMIVAIFAKrELBAdu/UKguut1QzplhUJ8dfdY3L+Du3JVpKRg1lsTQbcgYA3JqyQilRBg7X6SJDZ2jxSTpibfISKjeRMUr5KXUjlJ7YoRyRVcJlazxjiN9eqWTlohSfsgdUaGr3lmbbrLqj+r0QKAQKgRECFtuewWm3/4ZLEBJyeXZL0HMY3mGL/zmK9f9fkrx2w0Qy47oiBCamx5MnPCY7VF0fFyOOZolGi2So+OR+cJGy0JRHdGG9o82UsOLZqjVfNqbzkK/05uiMrt4O738GvSjFh8jaDSzLBF0X8Dq+ECgECgEIqOWTf0CmusV0lPADy1iU3EKWueHOAVlKqysZioflt65wT3arzLm8erruLMr4H44/VHySYJRC9HKJ4XEaFvR6cYmSvW5zjkJV06c+/ApyEYpPfYX4nroZGaFDerN1Qa7jC4FC4DgRQHPV+29uMkML75DNaZ0xvnyQZS5LvHeGMYYcBbSK6ruwekjdJ3qNivWda2wPBsNEkIXxsBUPQhMCGwpWtmJ0FpvsT3XZdxokmkwNM1R83JySa6ZE3E6NpmtwW6ofX5aMNIxbejdc58IVX6dB417YxJRe5wOoYwuBQuAwCPQ4/qZXn+LvnTvWMGa36hwZ5bI/p7rOrDr3sv2OnaU3GHhEEnRl2wq3M9Yc1qN4oc3FIqyHik9iEtaVRTJMXhpTXo7PGfZ2VY4n4/fCFZ9dhYJ2HRtwwJUUAoVAIbBLBGyq1WwRC/iQTUQdl39LsFA/LPGhKBFfiRUi6q6UsGeJz+1CZMlyeUoswezl2Uzxdg4VH2sRkckikXnamcTGPV7H5wwJVCYtyYtwde4CyBqjECgECoEpBCREqA0WUlGawO22bWbiuSA9VHzfk+Tzd3jjvYOPIb8+yV0nxl6njs/5921joEvDBrZIWISamZNvagTWVzi2FN8On3QNVQgUAheOwPVaJwEX1jVGOnzJPASw23T3okYB3JK7kps1l6fxFtGW7UvxDV2dk2QGY8V3DC6AUsa7evVqnELg8iPQS6Xc6bcluePlv+Wd3SEOzc7CJS53852NfMXEmUX5HftydaLKZGWSSTaaUnw7fNI1VCFwxgjI6uyLzSYwKHrmbltXOjej83QL6Iws645zjscPib2XlYF0bMTLFIYvIp0eYji0JsVW9W8dy1DxSbTB0LJIJOE4hqxKbuHe7B03Jsct6+ocX/e650Jg9wgcKqtTX8/3arcjgxxDVMl8BMRHtYmT7Yqse5nodqAsRHY+K26Z4HTWfYcsIi4ZKr7JWFw7XzmDkjhJM3PKGZSq3KKdqzaw94/9n/mW4pv/gtSRhUAhcFwI6PGpC4D/lT1oAa/ElvWeEYaVGyd5RWNOWcbH3BWfxBFF5YtEzTbFKKuT6OyjCflYhooPvRjFO9VDcVjALibZOVkXXf/3G8OLmnG141eSUnzrvSR1dCFQCBwPAiw9Fh95WhJdF0rWQ0BM9MHtFA1o8WQukq74/K4tEcU15sFEFoCpqz+LZWUSY8X33GapDUsfsLSo05xLWYZ+DbWZzdDC2sRSfOu9JHV0IVAIHBYBsUSMIISF0AmmWRg6cBNlDVcqWj7stI/26qyzP2+KRcnAsjit3/2nhISgO9OFgaLijny39jwoKZY396VEk6FydL3uAr1B6/ZuLFYcS5KVOCSpxtJCWIJIqm1wlokGtP09ML768SvJMsWHeFT1PYZsvlXgoBW6kr/0aB9pTawQKAQuGwJa1jxqxU2V9bfeU1cQruh7DruWOkkKSOshMVUUcP7GVcrSMobyBeURL5iYBkUmnjiWd2lxPBRjxscjymrrbYk0Pp/TlujRLTt1aVPdRYpPKwmTf802O350HdL103tKy6o518aN671SdXQhUAgUAseNgHX9OY1PGdcm3s5TFBbn7zUyA1mkC1sYLbP4uAr8zk9K66rxkyHDL8uElN0z7GJ8ikDVnAuBQqAQKAReWSqgi4HsSSULp9YsnHtVSYbOG7pDKFxfKJvE+FADqbfAkCAYOmXO1otUCBQChUAhcFoIoCwTZ3tWy/QU3joFEXPk4uQinUVisIniA4Q6Ds39uD21pTgGxpdTeEA1x0KgECgEjhkBjXk1cpW4MlV0foxzp6xv2VhaZrW22lTxuXm8eIBZVKNxjADVnAqBQqAQKASWIyCxURkBBXgKIiNUQtOL5052G8V359Z4UluL3uZ97nXruEKgECgECoFC4CAIbKP4EJryq2oV/2YDd+ewyNFNraryx+kmqPrAVhR5ECDqooVAIVAIFALngcA2iu/6reQBUmr9nt8g++pW9qCbr6AjChzZoHzGY9FS5GeS6K+kJUbFCs/jvau7LAQKgULgYAhso/iwJqCYIQrdFbcPBQOAqn2CMR1z+lAULOJv+61W7f/yg6FQFy4ECoFCoBA4GwTmKL6rJLlOI/tUle8/ltmQJ4/bUz+nobxREkXuvSOy4sKuKPG5qQHkJv3QJC89G8TrRguBQqAQKAQOisAyxfdqrRAQr9qrDmb5q0luk+TNk/xs+/tNkzxu4k6+ZsCZhw0AK8AbNBcphcrVqWCypBAoBAqBQqAQuBAEFik+HGmSVG7YZvGwJPor/WWS6zYi079vfG0OcZxGkmOh5Fh9b9isRIzdONe4ORXA97jghdxsXaQQKAQKgUKgEFik+CgnZKHkGxoj9zDxROsH7C2KHcm7J3nmAjjvluQ+7Tc9s7B2U5RIREsKgUKgECgECoELRWBK8Ym/sdJYfToxYGmZau6oBEGRo6QUBY+LGhj6zXiIUMkdknz7hd5lXawQKAQKgUKgEGgITCm+YWPCz03y8AVo4eh82yS63Up+WSTig9ygyh+I8oWPrCdQCBQChUAhUAgcAoEpxaeP0me1ybxdkhdOTOz1kvxT+zvrjRW3SPR6unU7XqYnWdgg8BAg1DULgUKgECgEzgeBKcU3dGGK5U25OTUh1HmXiPP17M4xcvdo7SF6MftD2gF6/X3I+cBcd1oIFAKFQCFwLAhMKb57J7l766YrG3NKdEDWCfklSa7Zuu+Oj2PlfU8rYr9fa02vju9t2oH6+enuUFIIFAKFQCFQCFwYAlOK78ZJfqLNQGLKv4xmw12pTxNr8IuSfOvEbPVFenxLYrnT4He0ZFhciO64SiNKCoFCoBAoBAqBC0NgSvH5GzemBJRbNCLqPiG/SXahwCS1qMt72Wi2OuCiL3tSO39YBiHR5Rmtjs9puv4qiygpBAqBQqAQKAQuBIFFdXzXaspPO3c1dwimJbSo6bt9ox4T2xt36EVWrU8f5aZB7VSJw80G9GbPa4rvRUkefCF3XBcpBAqBQqAQOGsEllGWcWV+bRJtg16R5K2T/GMSLC4IqMcuUK2J8G/K9pS40rM+xwC7puL19x78UD39zvo1rJsvBAqBQuDiEJhDUm02klwci6asWgdd3POpKxUChUAhUAjsGIG5im/Hl63hCoFCoBAoBAqBwyBQiu8wuNdVC4FCoBAoBA6EQCm+AwFfly0ECoFCoBA4DAKl+A6De121ECgECoFC4EAIlOI7EPB12UKgECgECoHDIFCK7zC411ULgUKgECgEDoRAKb4DAV+XLQQKgUKgEDgMAqX4DoN7XbUQKAQKgULgQAiU4jsQ8HXZQqAQKAQKgcMgUIrvMLjXVQuBQqAQKAQOhEApvgMBX5ctBAqBQqAQOAwCpfgOg3tdtRAoBAqBQuBACJTiOxDwddlCoBAoBAqBwyBQiu8wuNdVC4FCoBAoBA6EQCm+AwFfly0ECoFCoBA4DAKl+A6De121ECgECoFC4EAIlOI7EPCX8LJvkeTDkrx1kldL8sIkP5nkby/hva66Jd/VuyT5oCTXSPIvSZ6T5MlJ/n3VyfV7IVAI7BeBUnz7xfdcRr9TkgcNbvavk7x2ktdI8j1JvjLJS5eA8fFJnjATrP9IYvynJ3lUkh9L8v9mnnsRh/mmfjTJTdvFzO0vk1ytYXDPJN+e5L82nMz7JIHXhyZ52yRvnOQ/k/xVkme3zcYPJ/m7Dcev0wqBS49AKb5L/4gv5AZfM8l3JfmVJI9J8g9JvFsW54e2hfmGbXGemtCHJ/mk9sMnJ3nz9v+NZUHv8lpJ3iHJ9ZO8Svsjq/JmSf7tQu503kXeJsn9kjwyyVOblQejT0/yLU05fUbDZd6IyQcnuXeSG7QTnpXkD5P8TZI3SPKOSShFuFN6Nhs2HSWFQCEwQqAUX70S+0bgTZp1RoFdLwmLbZmwjt60HcCamXKVWuC5DVlRhLX5Jfu+kR2Nz/35C21D8EUzxmQ1f32SL27HPiLJfZoreXw6hWsD8hHth3u0Y2dcpg4pBM4HgVJ85/OsD3mnX9Dce3dti/iiuVw9yZ+3H/8sybWWTJoi+Ob2OzcqBfuyQ97kGtd+dJKbN8v1V5ecx8Llyr1xc5OyGJ+44jriqz+XV1qI5BOT/Pgac6tDC4FLj0Apvkv/iI/iBq+a5MXN2nvLluwxNbGPGyzsFvhPWDL790/ytMHvXH3PO4q7XT2JGzWL9WcH1tn4rFdtLlHHihPC5qdWD/3fR3xgkl9rx76guYc3jSnOvGQdVgicDgKl+E7nWZ36TJ+U5GOTfP6S2JPEj69pN/q1Se615KY/IMmvD36X6PHHJwKS+KQ46Ou12NyUwoYDPMj9W8xundv704HFLNb6i+ucXMcWApcZgVJ8l/npHte9yWTk8pSwws03JY9rrjm/yYr070Xy2Um+r/34r0lYlS8/rlteOhvJKUoe7tDcwMODxTBZs6w+yStvl+Sf1rw37k4JReRuSb5uzfPr8ELg0iJQiu/SPtqju7G7t6zE/9tq26YmOLRSVllwP5jk09ogrEkp/qckP5NENusPJPnM0cQfn+Qm7W8UFsW1rvQ4ovO+o2061h2jji8ELiUCpfgu5WM9ypu6TZLvbPVrMhVfMZrlGw0yOLkB33DJXcheVLOmRIDIYhQvOyXpivuXBiUK5v9O7d76t7lp7FJdZN8MPDzJ554SODXXQmCfCJTi2ye65zm2EgSuOkrpt1pSCySUG3xTg0S5giL0obB+WEFEPEpcakpev9XGSW4hD0ty6yOF2vf1Vkmu0xJ6xCR7Ib9MS8k7XJ7vNpi/+rtvaP/+o6YIN7k9rtKO0SmVe2xyr3VOIbAWAqX41oKrDl6CAIWnYLq76Bwqk1Ac7s6tDk1dGWHd/f1orC9vSRz+rMi71635t1iXbNCPam4/tGjkh5KI9R1jbO892vzedXCfYpFf3cowesnBHyR5z8ExPz9Q+mrybrvhW8dqVthOvjDJQzYcp04rBC4dAqX4Lt0jPcgNsWrUo6nDQ5/1FUkUWlNYlNVdmsXzfk0ZqjUb04wNY3arbkIWpKxH8bFjFNmr6u9YvQryKS/WLD5TjC1+hxVlPrRufY8swqu0m/q8JN+7wQ1Khnn+4LzrJvnNDcapUwqBS4lAKb5L+Vgv9Kak5nPhcauJ28nGHBdZX7MtvKjIMLGwDsciZvfO7Y+U5pDbk+Xo33+R5DeS/PYWXJf7Bocy475kbSnGR9w9LlcQk0RlRihIlGtkWMDv31heej3eOvOmML+7nYC+THH/MfGZrnMvdWwhsHMESvHtHNKzGxC3JlJmwtWpTm8s3jMKT8LKVPzudVq6PiXKHSiOx3I8RfnW5lo0d9maU1YpN+jvt5tjuXJ/ErG+Zw5umuWmy8W6MiwL2cZduu516/hC4CQQKMV3Eo/pqCfJYumdCN4+CaaQsbD4XtT+OI7f+TMOz07dxcJh6ZyicO2+pFm0iullZI6zV93XZzUCa/8fObfyBQK/oXXINWq8dUTiEEvz1dtJlOwz1hmgji0ELjsCpfgu+xPe//1RaBTbMm5NMS21dkTxuiL2oUi+YCmRb0tyx/1Pey9XUHvYFf/3J7nlgqs8oCX8cOFyjXblxvL9xxYbdaqkF8kv6wgC6173p20TJVtSCMxFACOSDZh351hFyIQ3xZqxUX/LUnzH+mhPZ15iSFyYy3gnFWF/VSORFm8a9+aTwNHrzG41YGQ5HRReOdOhC3NZZwRWLT5NbZw6mXS/V/FL5SCEG/mxa4CA1FvDW70QlYu8e0uuWWOIkz4Un6nSlvdtcU2sN1zKYsY/ctJ3tv/J8xA8sG06kU3cd+KSjlFmJEYtpi8mL0Nb/Fgog5tefF8mt+bL+xJeDR4VZBi+kbU9GqX49vVozmfcX25dBrjrek+94d1z/3lJWYVigZ8yAc3vJHmv9vdTds3ppkCpu2flGNy6Y9FPUH0emSozGFq/y+jdxuPKIFUMb0HS+sni5Nmcg8Bd70Pvlnun5GCM6OAWbSPw0+3/s6hLrogAQomfaO8M5ae0aExqboOm9rQTSzy3tdfiVreZtVnrIQqE9BK2NknMmvtsrBcypT173UvW4qItxTcX5jpuEQIIlH0oitV7wfTw2I8edBVQyN2TOvoxPrp/bt3aNZNF3HyqiS3uSdmAsg3uTGUdY1GcrkhdhiqX0riBLgVmI6D+T3zQDntZ6yLjyyC12OvkIDnIYr+qfdFleaOtYe7dQsvqoPB/b3Bz4qz6H4qXWig/ZkHc9bLgscl9SMDS8gqOn7pgAPj2EIX3moIcZwpjCjIGZWSDce1Bm7FN5rXqHMrYs8Vjy4PC2zFLSvHNgqkOWoKAZrA6gStRUFje++k5RcyKQkTGvIgv0s7NQk+wjYgxnLL4GFlePkLKa7hzhsPvtvo+PKM/vOBGZXNyHauPVOgv5qlYf7zQUJIWKp0sHMvKEfuA+bmIBbtnzn5Oc2uO711PR6tH+QAAD/JJREFUwk54rvlvjyefC0bL7pOVTFlRVLwRY0alfm5XfD/Z6lAXjdnj136/96DDyL6w7uT3rMvrzy1zKsW3r8dxXuOyNHw8Xj4+d1YMN5PYCkXADSqppTOscHveqUFkR945JdXy+bAIy6W35Tk1NBXsi2sqU/DxU35woOhYHn5nKS+Ta7REn86Eo4M9y09BPIXnd9mwNhf+ZjG3Cz+VZry7eKbWL4X6kopg0AkUpsaWdOQ4cT/YbZQUsYtJH9EYiCSEIeDh3cGwtEjUo3pn/bcsXjrsqWmz0TO+93XbNtuerVKoReVDV7p2Kb59PY7zG5cy8/FILLCocONRZOJc+DSHlg/2klVZY6du/dl9yrDsXeRZZFxtFOI68QhuU7FTC48FioXNlUTUTWpOKz5zjgv5sAxmFWcrnlh8sQRH6rm4gpetRFziPAnkvZs3YtuVa5jBjY3Jt75v8T19yJJwSym+fT+BGj82U2/W4nb7zOw6Fagluki/5kKSeLGtGI9Lk/Vy7n32vr5ZzzC9Xev+sQjf4SKP1Ua3kHMX3hUxT1awTMlxQssm+PQMbucq51HWs0zkBWAaEstW2sMKlSmO/UhyFm/ROC9gPJ7vwCaTCC/YcC+VsvhWIVS/FwLHh4BF/qFtWhYW7Z4sFGPi7+Ob+W5n1Bduo65qTcUT0WOfEpDwl56zcJdTMHhhEabrjrKtiNeLb79ui1Hj6V2UqKY0Qs1u34AgZ1feQycJf3Dx97ZjT04iSW6RDN2rrHrdSErxrQKhfi8ETgwB8QylIVPlI/1W8KdyBV5mQecmlkwkDi3L6hNblUlLZBGjxTtnkUTmHSE2UbdfEwyeB9iLMfM+UEw6pVBcEk563e6iYcUJJdbIXJbo1WkP+/FCBNzRypvEb3lNFsmQlH1RydQVzi2Lb82nXYcXAkeCgDgfHs5FzCzaEKkJvMwybL0k/qmgeZEok5H23oVL7ZTLZrZ9rpSUQnNyr5YZvM6Y8MbWNBSlBUqbkDAsE2QVveuIZBnlPVPSM75XKT4Wps0MUcxOWS6VUnyrEKrfC4HjRsCuW5wGwbU4DdeV3bgsT0kvFyWSm6SybypcXVy26whrwb0S5TTq+BYJ19owxqoQm+I8V0GO3rOmWXvddT4XD+xAElng6r2TXCJpyPPgglY2MkWwPszEdS2W3ViBDueADcazXWbxOV4WuDnJK6AIl0opvlUI1e+FQCEwBwHFymtTRw0GZgFIclhHWGzcvnMUnwV5SBg+1Qx5nWuf+rHfPGj2vCuaQBR5Nls2QRJmbjjqNgKzIa2fMgTZ38vEhg5BwyoWmE6daCzPemkbrlJ8p/761vwLgfNFQNF1j9WtcnUO3WEQY6lMdc44FzS5yXsLMSUHSg92IcMSE9YaovWhEqJklZ4QNHK8FbsQNGndKqQoh27tK41fim8XkNcYp4CAOrop7sy5c8dT+PC5B9dxF4KA4msFzGSd5BZ8qmJ+5yxDxTe78HsmYLJnZdESmZ1PGZyH7ux+7d/LKNJmXup/DtPhRBkVsRnqMb/JcUrxrQtvHX+qCKjvkca+qTw4yV03PbnO2wsCivd7mvs65QyLeGX3MskjHXRY0C/ZZJebOmUKd2j3PaYt25fiK1fnkb5ol21aCk4lJByLDDuZH2pOuygA3tfcjwGfXd/bpgXsGG+6m2/XczqV8SS2eCcIJaUEYVcyTJwZl0rsy9WJqk/dHxcnV+dSKYtvFUL1+yIESvFdGZlzVnwSGiiiTUUqPIW0jmiDo+iZrENZpjj6Cetc6BIeO6QNnLMpQgum60Xn2F0GydCa1I1ETV8XCTC9ufKc5JY50HNt9nZTSODRr5XiWwVC/V4IFAJbI3CIrM4iqd78semf1+vt5lC4sagwA6EVW7XB642WzW7chcQzQ7nXszmXlTPIznxRi91xaeO6nZJ3GpAX4B7VsaMU3yoQ6vdCoBA4WQSqLdFmj04Bv5IDbkGcmOrwlkl3JWqDtaw7g3E6Cbu4mzrTcYbl0N25rIC9t5PS6gw7TO/uMp4nBqPHtj9+QWuBVopvs/eizioECoETQGDciBbn5JDUGO+jWDRLRY9DlsM5lzEMH+mPtbZBCvkViS9jshnG0FCNDTM1+5hKGSgg2ZWsQqxCvVfi+FUaUpZRpl1x9eN4EHCI6u5uc9O7SEy9kvpR3qP9QEHK9i3FtwqE+r0QKAROGgH0bci6NUvFzmJRfW6zEnRlwOiB6NgC22NBJ33DO5r8sIUQpdW5O6eGV86DDLoTBsiMZSnqOqI0RAd0BeuESxRd3rLaQHWUaPV6kpFNiX6Txqf09Oi0qdF5QZxwmWhhpsuDDY72XSulkltWQlQHzECA28SHg5VBEammqbqqe5FXxQNmDH/yh/jO1JlJxlBojVYJobLF+Bz76O3rgVosb91qyFgKKMwkZGiITBnWu3hF5L2Xf9jeTXRxun4sEwlMEoMktmFUYUUjqWYNcptKWvFOU3hzO4VQWJTfDVojYXE9nKvcpcoirCPLRJmSeyAU8yyavlJ8+/oEz2dcGVVcS72Q2I7bgkMBCmLzuR9T2cNFPxnfGMb43okaiwXSXQ1lFVJLK5dKXovyRT+Zuh4EWEisrX9rCvBPTwwWLlBW/ZOalThr+qX4ZsFUB61AADktt4nsMOnEYgViBndubO1SoO3ezlUE+LFVPDLJU5uVp+ZI7AKbDFJf6eXn3C3gXN+NY7jvb0zyZS2mhmnlVGKgNpPilJJftFla1p3jCjiX4juG1+5yz6EzNYi/eElLrogA96caNoW+GO1LCoGLRoAewNyiVdEPJ/mcE3DB4/i0nsgYxdqDF3S2lOKbDVUduCEC4n9qcfju33kN3/+GlzvJ0x6d5OZJrt/ioid5EzXpk0eA1XffJDo3DIvOj+3GxBa1MpJDwM3ZGwzPnmcpvtlQ1YFbIPB17UOScnyfLca5rKfeqCUFiLXYvZYUAodCAJm7xBXu92MVYRQZpI/ZdIKl+DZFrs5bBwFM7dKf7dIkwSztlbXOwJfkWCncaqmkhas7e94lua+6jULgKBEoxXeUj+XSTUqHZpmMxG7yWQvukJtl2AFBanRn3x+fggppWCc0i6roiJGFiZKHIWHwXUb8l1P9zYa3pHgXXZQaNlZklUoc8QOvqR0OgVJ8h8P+nK7MorEIi/ep2VlERqwD93WSaJOi6Fix8RsuSPW/cRL/UYC6aYtPIMc9VcFDiHUE04X+aESmp8Lgj2yWYP/bVGGwujVKT03VBzcL8lSxqHkXAntFoBTfXuGtwQcICEC/RRL0QvdagYwsRwWtBJv7sowtxfIWfcf/0gkjTplR4u6h33u/HSnmulWT5zfLcJhyrohYraTaSYpydlr3CeNVUy8ENkagFN/G0NWJEwiw6LjrsKVTdBq/9gWa9abYXbF2b1K5CEQURV/ZfrxtEt2ip+R1W6dlxd/Idpd2XT6CJ+Z7kzzAqsXegiJKETtBCaUeksuTO3gs2u8ofSBDqxnmT0xy3ZYVusiNfAS3X1MoBI4DgVJ8x/EcLsMsENeiPeKa7CKZ5fZJdMruClAn81U9vToru3HQTakrmpLOBI/WSJuVYxZ0buKQKJa6/GuSr27p4wh5uSjRPr3nxI3IYnMMges7NPfx9zUOStmg0rtLCoFCYAUCpfjqFdkFAvdOcvc2ECvmi9sCbpFnuV2l8eg5ZE7TSy67F7fxZDjKdJwScT2sE1hRJIIcq2C1UWyLrUWSDytWTI/rVxzP71dv3Ic4CnEhTgnF14mAbR7UM315kk9O8vhjvfmaVyFwbAiU4ju2J3J68xkyvFuYueu48bp4x8T1umK840z6Mq1FOv+nGB4S3LGoNcLgICmkW0PHhiDlxP3IFYtaCTfiuFyBtYbKjFCQWG6mZNhxHLeiBKBZ/ceODZSaTyFwSARK8R0S/dO/tvcHQbUEFK5M7rc/mbgtVFw4KQmLRfLKKunks46jTMWxhsKKRIYtW1T/r2NN3f/W1qLF3GVrTvUn4wbtPeRWWcSSXCS7EAW8GF9KCoFCYA0ESvGtAVYdeiUEKDwxKYKAGdfflHxvK1Hwm9KDOS1LuPIe1AaT7DKmUOLe0/XA2MogjlHQtL2kEXazYLlspwiANeyEH9FNepnbsrPgOJbiV7s37nB9jFjUnAqBo0GgFN/RPIqTnIh6O4qH6IP2sAV3gbUFe8uijMWp02Qp/kb7YSrF/wmtDYl4mLjYMQql9II2MY1Sb7lgkg9onSxkp3KNUpZTotyBxaiEg5VLJMewEksKgUJgJgKl+GYCVYdNIjB0YcpIlHI/FiUMFmqJHXg68XXOkddolozzZD+KkXVrSSIIl6qaNgk0x9rLbujCXMZTqvBc/R384Dgl4phimo9qlrAGq4gBlIloezTHip6Dex1TCFx6BErxXfpHvNcbtBjLTiRq03qcanhRbkh9+siqYvTxZLtC8HedmlmO5CGtTIKLkCI4VnmtVqfH5SnTtcc5h/MVF9Wwl3xhu7fx/cCWVcvy5Qq1AXDfMkLJ14+o3o4Vj5pXIXAUCJTiO4rHcLKTULPHLcc6k905ZnT3filv4LZ8bEu7X+dmUZB9STuhK45rt2a3L2zW3rE3b1XE/35JuDP1JhxLL9ZX8P/2rRP28BiZrTYAOmPbaLB+iWOf3WjgZNGy+v56HXDr2ELgXBEoxXeuT353941UGrn0d7TU+uHICs81uJR8wWJDnryOKIr/kXaCnnViXL/cGEymFO06Y1/UsVyXLLXnTLhlsdzoWM+d6940AR3K1VpROleuXn2SWYaC0QaLC9FD7Usv6qbqOoXAKSNQiu+Un95xzP3VW3alFPubtL5yXHsSX9CTsVBumkSvuXXlmq2JrfOwlbCaML88ro257niHOl5xvWxMiSiK/SkyCpGiU8Tu9/uPJqdcA2bXSnK9ZvGN53+NFuekOJFTcwEb22bk5Ye62bpuIXDsCJTiO/YndBrz8x7J6hSjEtdiqVi41ZnJOJTKv6kgXJbpSBRt/0eznNbuurzpBHZ0HotNcg9FRnB2io9SiOOsVBsHyh0lm/96ycjUVFh63MBd4EUhlhQChcACBErx1auxawSwiVy1UXPtouEsJhMWY5dFReC7vo99jUepoWQTj6PESwqBQuCCESjFd8GA1+XWRuDOzcXpxGWE1WsPXCcUAoXAeSJQiu88n/sx3bX41K2SPCWJTM2heD/FrfBR/nZz+3F3lhQChUAhsDECpfg2hq5O3BECsj2fNkG2jN4Lz+WNWkak5qwK4UsKgUKgENgKgVJ8W8FXJ+8AgdsleWiSfxgQOOtHpxOB91P5ghjfVHeGHVy+higECoFzQ6AU37k98eO7X/Vr0vnxWkqMkZavKP6ZrUXPDyY59iL140O1ZlQIFAILESjFVy9HIVAIFAKFwFkhUIrvrB533WwhUAgUAoVAKb56BwqBQqAQKATOCoH/Dxug7L/aKegLAAAAAElFTkSuQmCC" width="223" height="118" /></span></div><div class = "S5"><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="106" height="38" /></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 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" width="209" height="49" /></span></div><div class = "S5"><span class = "S2">where </span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" width="102.5" height="31" /></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 = "S9"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A = [  1    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0    0     0      ] ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">   </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">B = [  0   -alpha 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       1    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0    0    -1      ] ;</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">   </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">C = [  0    0    -alpha</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0    0     0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0    1     0      ] ;</span></div></div></div><div class = "S11"><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,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" width="199.5" height="32" /></span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">determinant = simplify( det( A'*n_t + B'*n_x + C'*n_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="E97C6163" data-testid="output_2" data-width="1141" style="width: 1171px; 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 usesymbolfont Linux 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="118.5" height="22" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">N_x = solve( determinant , n_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="944DCC9D" data-testid="output_3" data-width="1141" style="width: 1171px; 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;">N_x =&nbsp;</div><span class="MathEquation usesymbolfont Linux 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="60.5" height="66" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S11"><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="45" height="21" /></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="50" 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="46" height="21" /></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,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" width="51.5" height="38" /></span></div><div class = "S5"><span class = "S2">The two complex solutions </span><span style="vertical-align:-7px"><img src="data:image/png;base64,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" width="66" height="21" /></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 = "S13">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 = "S13">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 = "S14">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><div class = "S0"></div><div class = 'SectionBlock containment active'><h1 class = "S1"><span class = "S2">1.2)</span></h1><h2 class = "S4"><span class = "S2">a) Transient diffusion in one dimension</span></h2><div class = "S5"><span class = "S2">Neglecting the variations in </span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">y</span><span class = "S2"> leads to a second order PDE with two independent variables</span></div><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="152" height="40" /></span></div><div class = "S5"><span class = "S2">so we can determine the type from the discriminant</span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="103" height="20" /></span></div><div class = "S5"><span class = "S2">of the second order differential operator</span></div><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="207" height="40" /></span></div><div class = "S5"><span class = "S2">which is in this case</span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="161" height="20" /></span></div><div class = "S5"><span class = "S2">Thus the equation (5) is </span><span class = "S14">parabolic</span><span class = "S2">. We can also convert it to a system of first order equations</span></div><div class = "S3"><span style="vertical-align:-33px"><img src="data:image/png;base64,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" width="180" height="77" /></span></div><div class = "S5"><span class = "S2">which in matrix form reads</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="213.5" height="41" /></span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A = [  1   0   </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0   0    ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">B = [  0 -alpha </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       1   0    ];</span></div></div></div><div class = "S11"><span class = "S2">and compute the characteristics by </span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">dx dy dt</span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">determinant = simplify( det( A'*dx - B'*dt ) )</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="E8714D6E" data-testid="output_4" data-width="1141" style="width: 1171px; 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 usesymbolfont Linux 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="39.5" height="20" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S8">Dt</span><span class = "S10"> = solve( determinant , dt )</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="08310B4D" data-testid="output_5" data-width="1141" style="width: 1171px; 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;">Dt =&nbsp;</div><span class="MathEquation usesymbolfont Linux 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="34.5" height="39" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S11"><span class = "S2">We receive the typical result for </span><span class = "S14">parabolic</span><span class = "S2"> equations, </span><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="50" height="36" /></span><span class = "S2"> , representing the infinite speed of information spreading.</span></div><h2 class = "S4"><span class = "S2">b) Steady diffusion in two dimensions</span></h2><div class = "S5"><span class = "S2">Neglecting the variation of </span><span style="font-family:Symbol, 'DejaVu Serif', 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="145.5" height="40" /></span></div><div class = "S5"><span class = "S2">The discriminant</span></div><div class = "S3"><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="235" height="20" /></span></div><div class = "S5"><span class = "S2">implies the equation (7) is </span><span class = "S14">elliptic.</span></div><div class = "S5"><span class = "S2">Using the same auxiliary unknowns as in 1.1b) we can eliminate </span><span style="font-family:Symbol, 'DejaVu Serif', 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="164.5" height="77" /></span></div><div class = "S5"><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 = "S10">A = [ 1  0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">      0 -1 ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">   </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">B = [ 0  1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">      1  0 ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">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="82BE7587" data-testid="output_6" data-width="1141" style="width: 1171px; 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 usesymbolfont Linux inlineSymbolicElement" style="font-size: 15px; white-space: nowrap; font-style: normal; color: rgb(64, 64, 64);"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAAAoCAYAAADtylhqAAAKzklEQVR4Xu1cfXBcVRU/523SkNCIlqR8SvmqoBGlTQVrsnvPS0toiwWkVq0IAwoioA6IgKLD51RQAcXRwQpFqqAMZYBisVA62XOX0EyBwIAiUgQ/+PCPAgKJXdNk33FO5r7OZtndfMy+zdfev9q979537u/9zrnnnnNuECqtgkDECGDE81emryAAFZJVSBA5AhWSRQ5x5QXTgmREdKCInI2IywDgSBGZAQCvAsBDiHgtM+u/K604Auj7/olBEJyKiAsBYF8A+C8APC0iv7LW/r7Q8ClPsqamphkNDQ09iNgvIhf29/dvEJGBmpoaJdzPAWAgCIJ4KpV6vsKywggQ0ZUAcAUAPAwA3+np6dleV1d3sOd51yLiiSJys7X2vHwzTHmSEdEeAJAWkW9Za3+SDQIRnQUAt4jII9ba9grJipLsOhE5vaamZu7mzZvVgg02p8TPI+KhQRC0pFKprbmzTHmSKQiNjY1bPc9b0dHR8c8ckqnJ/7das8bGxj3Wr1+fqRAtPwJE9HUR2c9a+73cJ4jolwBwjohcYa29etqRrBhp2tvb99y1a1eviPQjYh0zD1RINnoEiOjHAPBtALiSma+aMCQjIsmzHJ+ZefTLHNuIRCIxz/O8p0QkZa01Y5tl/EYRkWKVK/dVzKz+U9maMWaD88varLXJiUSyn6owIjIfEeNOsLKSLNRARFySTCbVoZ1UTbcwADhcRGYj4ionfFlJtnDhwlk1NTWv6ymTmfXU+Z427j4ZEamZVXOrrWwkSyQScz3PexYA7mRmPQBM2kZECwDgifEgGRHdKiKrPM+bn0wmX6iQzCHQ0tJSX11dnQKAd2pra4/ftGlT36RlGACMF8mMMach4m2IeHIymXywEIbTzpK5kMYfROR91dXV7Vu2bHlnMhNMZR8PkhHREgC4DwDOYuY7i2E4rUi2dOnSmnQ6fb+IzJoqBBsPkvm+f3wQBPci4leHI5jKFznJjDGfAIALENGISCMi7gCAJzXazsxbivlkRKTpngMKaEkjM79BRF8AgHwpDfW1vhSOVYLt3LnzPkRsBIDjmPntsM8Yc3Ymk3m4s7PzXxPRqsXj8f1isdglInICIn4QAHoB4AURWWetXUtE8/P5ZEQUxgELLWsQw7CTiDSEE8t5+CVmPjz8LZFItCPifSJybiqV+k34u+/7TSJyFDPflfuySElmjLkYAK5DRE9EAgDoBgBd1GGI+CGNq7j8V17Hn4iuAYAPAIASaW8n/BYFeMaMGZdq5Dkej8+PxWJf1uCz7hwi8igiPhsEweMhCCHBAGCfTCazuLOz8z/ZQBDRP5zZ17knVDPG+PpRAWAvFUxEtgPAS6os7mS+OQiCazzPeyzX8Xe+57Uuz7jC9f/NpYYgxDBL2W5CRCXZyU6512iwOox9GWOOA4D7EfF8Zr49B8MzHIatZSOZcwpDpj83MDBwSmdnpwI02IhoMQCsF5GnELHN/Zz3dOn7/goRucc98xwALGDm/4VzaVC1r6/vaUSsTqfTH9+2bdu7YV9zc3P1zJkzFZhlIrIZEYcQzH245Yh4klrWicQw3/ePCIJA8akTkXcR8fPM/FAWhmph7hGRN7MwfE8Iw2U91ErvAwBvAsCB2fhlr9mFJF4TkS5rbfhdwPf9RSKyUUTeQsRHc3ESkUM0P8zM5SHZ4sWL9xoYGFDr8H4A6AuC4MOpVOrvuYIRkWqMauluq1soGEtEvwYA1RZtNzHzBVkaqBqnYQiy1g4BgIj0Q7w4AvLoFjqhSGaM6UBE3ynCF/NVOmiFCQD8FQD2zLVk2Ws2xqxGxMvcb2fmWqIs4oYhpZXMHCq2GoU7AODUYXB8rGwkM8Z8AxF/5gS6g5lPKyScMWY7Is4tZsm0T01/VVXVM4h4iIhotuB4a+0jxhi1Qg/otszM3x0BmSbFI4lE4igXx9Mt8hVr7RzdLfMJT0S3OCXT7rzB2La2tjmZTOZl57o8Ya09Js9cSEQvikgdIh5UqjRbJD6ZMeZBV7ul6ziDmdcV+rIazAOArwxHMu33fb9FRKw6pyLyOiKqCdf/v9bb23tsd3d3/6Rg0AiEVH8WEX/kHr2dmc8sgqEecH5bzJJpnzHmAURc7izjMdbaMIA7ONSFJTaJyNXWWi3rKUmLhGTZp0IR+ZS1tqsIQLqYMNc2bMQ/2+yLSNoB1jzV6sGytycRucxaqw583ub7vp7cw5xvwbRSSKJCxHUkXOp53sEdHR2vlYRhuSEMIroUAPLmn0bywr6+vlVdXV1pItKPr3VcEATBR4oRYLRpJXXk6+vrlbTNTqZfMLPm8MrSfN8/Qatsx/oyEVmda0HyzUVEmwBAA566XZ5nrb25iKKONK00uB3q6V4VdNeuXQd2dXW9pfO2trYeFIvF1G++31obnkTHuswh44ZYMqc96oyPte3LzL1RkkwFM8Z8ExFvch+gJ5PJHN3Z2fnyWIUezTgiOgcAbhjNmOxnRWSltVYJVLRFRDLFLnsbvpiZr3eY/gAR1act+QFo0m2XqnFVVVWa2NYQhh7JVdO3zp49OzGVig6j2C4Vq0WLFu2dyWQ0yK07jQZa5zY1NVU3NDS8AgBvW2uPLHTAGE4xCvVHQrJROv7ZJ6PhfDKPiDo0ThYEwTxEvF7rmBzRLrfWavB2SrRROv4aWtAQg7ZhS32MMesQ8XSH2zJEnOXGX8jMgyVYpWxRkSw7hDEkvZMrvDHmBRf9166iJDPGXIKIPwSAs5n51ng83hiLxf7kLNqAO2QMOTGVEqxyzhWPxz8Wi8WecUQoGsIwxqzRPOJISUZEnwSA8DCmAVYlmSrt/tnptlKtNxKSjTQYmxXjCtdTkGREdLSIbEPEPzLzZ8IBxpil+pv7GNt7e3vndXd37ywVQOM5DxFplSmpDHoVLZVK/S5XnpaWlv2rq6u1jmvmSEmmzxljNJMwT2OOiIgicpu1NgwllXTZkZBMJUwkEqd7nhfGx/4cBMEpqVRqd+Q9kUi0IaJGlHWRqkkFLZkrz9GkuuYvNQm7O6mrg4hIr7ad7+ZYw8xfKylK4zQZEekd0e4wreR53ueyK3hbW1sPjcViiuGcLAyH3S4dZoM3tcKlIeKCZDKpueWSt8hI5rQlN0GuRHkDEQ8DgCM0lwgAFhFXO0t0NyKqA6pJ2RtczlJDKpr8XuKS348HQbAulUrpNqkE+77eogGAc1UjQ6JppUIQBGsne/xMldHzvHvDBLmrvtCTdAMiavXFq4h4UZjb1ZwjIg5eS+vp6bm8kFVvbm6uq6+v17LpvUSkUAagJISLlGSOBAv0zqO78KBlNm8joia51Ve7jYi0L6zCCBf1HDN/NLxqlWelu/Nqw5QDLWfmjSVBahwnCUt9AODTAKClPnqy1pjWhnQ6fWNtba1WtOTzRYeU8uQuwRizFhG1gqVgLrMUy46cZKUQsjJHNAgYY/6ihyZEPKBQVUYp3lwhWSlQnIRzJBKJhOd5VkRutNZeFOUSKiSLEt0JMPfKlStjO3bs0DSYVlFpSdBgM8bcDQCf1fARM2shY2StQrLIoJ0YE2f9LZDdfxDF9/1jgyDQw8FGa+1JUUtaIVnUCI/z/Fkk01q0jYiot7M0P62H8eZCdyVLKXaFZKVEcwLORURVAHCXiByDiLNFRP8iz5Oe512eTCa3lUPkCsnKgfI0f0eFZNOcAOVYfoVk5UB5mr/j/1/AR3RALQrGAAAAAElFTkSuQmCC" width="76.5" height="20" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">Dx = 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="029BE042" data-testid="output_7" data-width="1141" style="width: 1171px; 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 usesymbolfont Linux 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="59" height="40" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S11"><span class = "S2">does not reveal any real solutions, so the system is </span><span class = "S14">elliptic </span><span class = "S2">as well.</span></div><div class = "S5"><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><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">1.3) Korteweg-de Vries</span></h1><div class = "S3"><span style="vertical-align:-18px"><img src="data:image/png;base64,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" width="194.5" height="40" /></span></div><div class = "S5"><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="106.5" height="38" /></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,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" width="211" height="116" /></span></div><div class = "S5"><span class = "S2">Further we define a vector of unknowns </span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="100" height="31" /></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="199" height="49" /></span></div><div class = "S5"><span class = "S2">where</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A = [ 1 0 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">      0 0 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">      0 0 0 ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">  </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">B = [ 0 0 1</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">      1 0 0</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">      0 1 0 ];</span></div></div></div><div class = "S11"><span class = "S2">The characteristics</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">determinant = simplify( det( A'*dx - B'*dt ) )</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="785D3439" data-testid="output_8" data-width="1141" style="width: 1171px; 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 usesymbolfont Linux 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="33.5" height="20" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">Dt = solve( determinant, dt )</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="6A477364" data-testid="output_9" data-width="1141" style="width: 1171px; 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;">Dt =&nbsp;</div><span class="MathEquation usesymbolfont Linux 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="38.5" height="60" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S11"><span class = "S2">are again typical for </span><span class = "S14">parabolic</span><span class = "S2"> equations.</span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">1.4) Accoustic waves</span></h1><div class = "S3"><span style="vertical-align:-52px"><img src="data:image/png;base64,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" width="466" height="116" /></span></div><div class = "S5"><span class = "S2">First we use the definition of the speed of sound (11c) to eliminate pressure</span><span style="font-family:'DejaVu Serif', serif; font-style: italic; font-weight: normal">p</span><span class = "S2"> from (11b) to reduce the problem to a system of two equations with two unknowns. We apply the chain rule</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="130.5" height="38" /></span></div><div class = "S5"><span class = "S2">The reduced system is then</span></div><div class = "S3"><span style="vertical-align:-34px"><img src="data:image/png;base64,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" width="227" height="79" /></span></div><div class = "S5"><span class = "S2">or in matrix form</span></div><div class = "S3"><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="178.5" height="41" /></span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S8">syms </span><span class = "S9">u rho a</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">A = [  1      0  </span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">       0      1    ];</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10"></span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">B = [  u      rho</span></div></div><div class = 'inlineWrapper'><div class = "S7 lineNode"><span class = "S10">     a^2/rho  u    ];</span></div></div></div><div class = "S11"><span class = "S2">The number of real characteristics</span></div><div class = 'LineNodeBlock contiguous'><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">determinant = det( A'*dx - B'*dt )</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="2DBC8FCB" data-testid="output_10" data-width="1141" style="width: 1171px; 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 usesymbolfont Linux 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="228.5" height="23" style="vertical-align: bottom;"></span></div></div></div></div><div class = 'inlineWrapper outputs'><div class = "S7 lineNode"><span class = "S10">DxDt = simplify( solve(determinant, dx) / dt )</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="AF59BB84" data-testid="output_11" data-width="1141" style="width: 1171px; 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;">DxDt =&nbsp;</div><span class="MathEquation usesymbolfont Linux 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="60.5" height="41" style="vertical-align: bottom;"></span></div></div></div></div></div><div class = "S11"><span class = "S2">equals the number of equations, so the system is </span><span class = "S14">hyperbolic</span><span class = "S2">. The result confirms that if </span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAmCAYAAABTahxxAAAEeElEQVRoQ+2ZZah1RRSGn88WW7EFFQMDCxXMH3bxWViYIHYgtiKIotgodiGIgYGKBQYWBrYY2GAgJmIjislzWRv2d++Zfc4+y++Xs+DC5s6sNWveeWfFnGlUSSEwLaVdlakAJklQAawAJhFIqlcGVgCTCCTVKwMrgEkEkuqVgRXAJAJJ9crACmASgaR6iYGPA5tPsn04cE1hvSuAI2NsOeDTpF+jqM8H7AtcPcrkEebMDuwCbAdsACwJuMZvwJfA+cD1k+2UADwbWBDYBFgrlDYEXig48hywEfA9sPAIzmamLAocHX/6r58Z0caBwFkB2heABPocWCYOSfsS5KpRAWzm3Q9MB/6O0/h1gKc68BMwL/DkAOZmNtfWXRY4DjgYmDtYfi5wbWKBBYC7gC0BgTsBuB34J2yuD7zURaBhSeSzOIX3gVUKjq4MOK5cEptM7GmK6mrAScA+wGzAu4DAudE/EgstBjwGrAG8DmwfV7Vt8rAIEX8B8wNTCNQFoFflm7B2B7BXwdk9AMeV/YGbE5tqqxqHTgZ2jn++ApwD3Bc3IrPMLMCjwBbBPJkmAyeLMe8g4B1g9UELdgG4NfBIKJ0KnFfwWDacEmNrAm8ldqY/W4W9zcLOUwGcbGmuVmKJCdVjgYvDyG7A3QWDrwHrALcA+/UFUFAERzEzPVxY5CFgW+D3iIN/jrG7WYFdAQ9Kh5UHA7jnx7DXpWL8/ATwCr8KrFeYPCfwM2B2Pr4F+AzTuxjotfR6Kqb0rwoLmeKXGOLMMAzeBox1Jqs74+DeHKY05vghrcTj95TSJOwK7Mvx7W3wJkyRLgA/BFYEvg6ABukv3gL2hogX4+zLWssT/wA4MdgnmDNDZPYOYdiDd3+D5NBW3bsQ8EMfAC0gf4SJ30wMttsUFtkJuDfGjgKuHHPHm0bcMxMqMtKEIRvHCQklN+YAvgPmAd4DVu3w91Zgb+AjYIXSvBIDzYBN7LkMOKZgQMCOiDGLbgvqjJiEzLx7AsZFnbcDuCk6goxtdVcKlvv9ALBjwaBAG5psCqwTd+8LYLs0OS3YMNmGhbPBeJHIjtZJv2R3GPrLR1FrhzBXbOYi4LrkGusClkPKbcGwQS4fANwYA6X9TwyXGCjiXh/lTOCMAatcEPHKIeOlBfV/LWZK2W8bZdfg9bsUsPf2u6942N+G0hvA2gMMWP9aWC8VY10VSBFASwlrIMUTsw9uYpGgm9YtcDeOOYLttZtZIrsN6tZvVgQy3YcNazmvWh95AmhqTA/HENWIMdHqY+lWT9+VaDp/WH8mHhM0bqvmwsYlF7cyvzxaIcdfBJ4NkJuius+mRp1rpragtbUznskmGdNHjLNPB6PV+zjiouz0it8TfbZ9t61iA/CFgzJ2VxljAPX6Gmg9dV9aZKV1k4s0fWLb+WGZrc9Gu+Z6kD496YMPAX3FrHp66HoAhgMfDSzFbBWb5qCx6+1rnrZmWGvYY0Jfx/538yuAySOvAFYAkwgk1SsDK4BJBJLqlYEVwCQCSfXKwCSA/wLC7con9hxoTQAAAABJRU5ErkJggg==" width="40" height="19" /></span><span class = "S2">, the flow is subsonic so the presure disturbance at a point can travel in two directions - upstream and downstream...</span></div></div><div class = "S0"></div><div class = 'SectionBlock containment'><h1 class = "S1"><span class = "S2">Additional reading</span></h1><div class = "S5"><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 #####
%% 1.1) Time dependent diffusion equation
% $$\frac{\partial \phi}{\partial t} - \alpha \left( \frac{\partial^2 \phi}{\partial 
% x^2} + \frac{\partial^2 \phi}{\partial y^2} \right) = 0\quad \quad (1)$$
%% 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).
%% 1.2)
%% a) Transient diffusion in one dimension
% Neglecting the variations in $y$ leads to a second order PDE with two independent 
% variables
% 
% $$\frac{\partial \phi}{\partial t} - \alpha \frac{\partial^2 \phi}{\partial 
% x^2} = 0 \quad \quad \text{(5)}$$
% 
% so we can determine the type from the discriminant
% 
% $$D = B^2 - 4 A C$$
% 
% of the second order differential operator
% 
% $$\mathcal{L}^2 \phi = A \frac{\partial^2 \phi}{\partial x^2} + B \frac{\partial^2 
% \phi}{\partial x \partial y} + C \frac{\partial^2 \phi}{\partial y^2}$$
% 
% which is in this case
% 
% $$D  = 0 - 4 \cdot 0 \cdot  (-\alpha) = 0$$
% 
% Thus the equation (5) is *parabolic*. We can also convert it to a system 
% of first order equations
% 
% $$\begin{array}{rrlr}\frac{\partial \phi}{\partial t} & - \alpha \frac{\partial 
% P}{\partial x} &= 0 &\quad \quad \text{(6a)}\\\frac{\partial \phi}{\partial 
% x} & & = P &\quad \quad \text{(6b)}\\\end{array}$$
% 
% which in matrix form reads
% 
% $$\mathbf{A} \frac{\partial}{\partial t} \left( \begin{array}{c}\phi \\ 
% P\end{array} \right)+ \mathbf{B} \frac{\partial}{\partial x} \left( \begin{array}{c}\phi 
% \\ P\end{array} \right) = \mathbf{C} \left( \begin{array}{c}\phi \\ P\end{array} 
% \right)$$
%%
A = [  1   0   
       0   0    ];

B = [  0 -alpha 
       1   0    ];
%% 
% and compute the characteristics by 

syms dx dy dt
determinant = simplify( det( A'*dx - B'*dt ) )
Dt = solve( determinant , dt )
%% 
% We receive the typical result for *parabolic* equations, $\frac{dx}{dt} 
% = \infty$ , representing the infinite speed of information spreading.
%% b) Steady diffusion in two dimensions
% 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.
%% 1.3) Korteweg-de Vries
% $$\frac{\partial u}{\partial t} - 6u \frac{\partial u}{\partial x} + \frac{\partial^3 
% u}{\partial x^3} = 0\quad \quad \text{(9)}$$
% 
% 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.
%% 1.4) Accoustic waves
% $$\begin{array}{lrr}& \text{conservation of mass: }  & \frac{\partial \rho}{\partial 
% t} +u \frac{\partial \rho}{\partial x} +\rho \frac{\partial u}{\partial x} = 
% 0 & \quad \quad \text{(11a)} \\ & \text{conservation of momentum: } & \frac{\partial 
% u}{\partial t} +u \frac{\partial u}{\partial x} +\frac{1}{\rho}\frac{\partial 
% p}{\partial x} = 0& \quad \quad  \text{(11b)} \\ & \text{speed of sound: }& 
% \frac{\partial p}{\partial \rho} = a^2& \quad \quad \text{(11c)}\end{array}	
% $$
% 
% First we use the definition of the speed of sound (11c) to eliminate pressure$p$ 
% from (11b) to reduce the problem to a system of two equations with two unknowns. 
% We apply the chain rule
% 
% $$\frac{\partial p}{\partial x} = \frac{\partial p}{\partial \rho} \frac{\partial 
% \rho}{\partial x} = a^2 \frac{\partial \rho}{\partial x}$$
% 
% The reduced system is then
% 
% $$\begin{array}{lr}\frac{\partial \rho}{\partial t} +u \frac{\partial \rho}{\partial 
% x} +\rho \frac{\partial u}{\partial x} = 0 & \quad \quad \text{(12a)} \\ \frac{\partial 
% u}{\partial t} +u \frac{\partial u}{\partial x} +\frac{a^2}{\rho}\frac{\partial 
% \rho}{\partial x} = 0& \quad \quad  \text{(12b)} \\ \end{array}	$$
% 
% or in matrix form
% 
% $$\mathbf{A} \frac{\partial}{\partial t} \left( \begin{array}{c}\rho \\ 
% u\end{array} \right)+ \mathbf{B} \frac{\partial}{\partial x} \left( \begin{array}{c}\rho 
% \\ u\end{array} \right) = \vec{0} $$
%%
syms u rho a
A = [  1      0  
       0      1    ];

B = [  u      rho
     a^2/rho  u    ];
%% 
% The number of real characteristics

determinant = det( A'*dx - B'*dt )
DxDt = simplify( solve(determinant, dx) / dt )
%% 
% equals the number of equations, so the system is *hyperbolic*. The result 
% confirms that if $u<a$, the flow is subsonic so the presure disturbance at a 
% point can travel in two directions - upstream and downstream...
%% 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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