Timeline for Fundamental solution for a parabolic PDE with constant coefficents
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2015 at 11:52 | vote | accept | foo90 | ||
| Jul 28, 2015 at 6:33 | comment | added | Andrew | @foo90 For the equation $u_t+(-1)^m\Delta^{m}u=0$ the fundamental solution is the inverse Fourier transform of $e^{-|y|^{2m}t}$. For $m>1$ it can be expressed through hypergeometric functions. Say, for $n=1$ and $m=2$ Mathematica gives $$ \frac1{\sqrt{2\pi}}\left(\frac{2 \Gamma \left(\frac{5}{4}\right) \, _0F_2\left(;\frac{1}{2},\frac{3}{4};\frac{x ^4}{256 t}\right)}{\sqrt[4]{t}}-\frac{\Gamma \left(\frac{3}{4}\right) x ^2 \, _0F_2\left(;\frac{5}{4},\frac{3}{2};\frac{x ^4}{256 t}\right)}{4 t^{3/4}}\right). $$ | |
| Jul 27, 2015 at 14:16 | comment | added | Andrew | @foo90 Not off top of my head. | |
| Jul 27, 2015 at 14:02 | history | edited | Andrew | CC BY-SA 3.0 |
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| Jul 27, 2015 at 9:47 | comment | added | foo90 | Thank you very much. Do you have any reference? | |
| Jul 26, 2015 at 21:54 | comment | added | foo90 | And for an higher order parabolic equation there exists a similar formula? | |
| Jul 26, 2015 at 20:37 | history | edited | Andrew | CC BY-SA 3.0 |
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| Jul 26, 2015 at 20:24 | history | answered | Andrew | CC BY-SA 3.0 |