Timeline for Cauchy problem for an overdetermined system of PDE
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 12, 2015 at 20:34 | vote | accept | guido giuliani | ||
| Jan 7, 2015 at 20:13 | comment | added | Deane Yang | By the way, why is this system overdetermined? Don't you have 3 equations for 3 unknown functions? | |
| Jan 7, 2015 at 20:12 | answer | added | Deane Yang | timeline score: 3 | |
| Jan 7, 2015 at 18:42 | comment | added | Deane Yang | I can post an answer assuming that $z_1, z_2, z_3$ are real. But are you assuming that? | |
| Jan 7, 2015 at 15:14 | comment | added | Igor Khavkine | Your problem is very concrete. You can get much more out of writing down explicit formulas first and proving theorems about them later, than the other way around. In particular, you can take the Fourier transform in the directions parallel to the initial value surface and solve the problem as an (overdetermined) ODE, where most of the conceptual difficulties are absent. | |
| Jan 7, 2015 at 14:51 | comment | added | Ben McKay | You might take a look at Deane Yang's book Involutive Hyperbolic Differential Systems, which proves a version of the Cartan-Kaehler theorem in the smooth category. (I haven't yet even looked at your pdes, so I don't know if this would apply.) | |
| Jan 7, 2015 at 14:30 | comment | added | guido giuliani | @BenMcKay What about the smooth category? | |
| Jan 7, 2015 at 14:25 | comment | added | Ben McKay | If you are willing to work in the real analytic category, you could apply the Cartan-Kaehler theorem, if the initial data surface is not characteristic. | |
| Jan 7, 2015 at 12:03 | history | asked | guido giuliani | CC BY-SA 3.0 |