Timeline for Posing Cauchy data for the heat equation: $t=0$ a characteristic surface?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2020 at 14:30 | review | Low quality posts | |||
| Feb 12, 2020 at 18:20 | |||||
| Sep 11, 2010 at 11:08 | comment | added | Willie Wong | Sometimes it is possible to pose data on characteristic surfaces, but to establish existence and uniqueness of solutions for them requires additional hard work not covered by standard nonsense. See, e.g. the papers of Cognac and Dossa on the initial value problem for the wave equation with data prescribed on a characteristic cone. | |
| Sep 11, 2010 at 11:06 | comment | added | Willie Wong | You can pose Cauchy data anywhere you want. The question is whether solutions exist and are unique. If you just look at first order linear equations, you immediately see that at least one of existence and uniqueness will fail. For more general systems of PDE, you have the theorem of Cauchy-Kovalevskaya which guarantees existence and uniqueness of solution for analytic initial data posed on noncharacteristic surfaces, conditional on the fact that the top order transversal derivative in the principal symbol is nondegenerate. | |
| Sep 11, 2010 at 8:24 | history | answered | Anand | CC BY-SA 2.5 |