Timeline for Classification of PDE
Current License: CC BY-SA 3.0
5 events
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| Apr 11, 2017 at 22:28 | vote | accept | AFK | ||
| Jun 13, 2011 at 15:07 | comment | added | Ben McKay | Sorry if I misinterpreted the question. I hope my answer is still of some interest. Gabber's theorem doesn't really tell us anything about classification, but it is one of very few results that hold for a very broad class of differential equations. If you are interested in general theory of differential equations, independent of considerations of ellipticity, hyperbolicity, etc., then Gabber's work is worth thinking about. | |
| Jun 6, 2011 at 17:29 | comment | added | Deane Yang | I'd like to add some clarification. I believe the original question is for a single equation for a single unknown function. So the symbol is always a scalar polynomial. The associated tableau is always involutive. The books of Bryant et al and Gromov discuss involutivity in the context of systems of PDE's, especially ones where the number of unknown functions is not necessarily equal to the number of equations. I don't think anything in these books are particularly relevant to the discussion here. Also, I don't really understand Gabber's theorem, but I'm pretty sure it's not relevant. | |
| Jun 4, 2011 at 21:02 | history | edited | Ben McKay | CC BY-SA 3.0 |
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| Jun 4, 2011 at 20:57 | history | answered | Ben McKay | CC BY-SA 3.0 |