Timeline for Decay of weak solutions to degenerate parabolic PDEs on manifolds without boundary [closed]
Current License: CC BY-SA 3.0
11 events
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| Sep 22, 2014 at 14:11 | comment | added | TomJoseph | @MichaelRenardy Did you miss that the estimate is desired on compact manifolds? On bounded domains yes of course there is plenty of work as I indicated in the OP; otherwise the quantity of literature is small. I am not sure how your somewhat rude comment gathered five upvotes. | |
| Sep 22, 2014 at 14:08 | vote | accept | TomJoseph | ||
| Sep 18, 2014 at 5:57 | history | closed |
Michael Renardy Stefan Kohl♦ Daniel Moskovich Willie Wong S. Carnahan♦ |
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| Sep 16, 2014 at 15:00 | comment | added | Willie Wong | On a compact manifold without boundary, $u \equiv 1$ is a solution to the porous medium equation that lives in any $L^p$ space. So you cannot prove any estimates of the form you wrote with $f(t)$ decaying, at least without further assumptions on the allowed data. | |
| Sep 15, 2014 at 2:00 | review | Close votes | |||
| Sep 18, 2014 at 5:57 | |||||
| Sep 15, 2014 at 1:42 | comment | added | Michael Renardy | Questions like this always leave me with the impression that the poster has not done his/her homework to an appropriate extent. I mean, there are only about a bazillion or so papers in the literature about porous media and similar equations. So in a question like this, I would rather expect something along the lines of: I have read Refs. [1]-[20], and I have concluded X, but this still leaves Y unanswered. | |
| Jul 16, 2014 at 21:03 | answer | added | riem | timeline score: 0 | |
| Jul 11, 2014 at 7:43 | comment | added | TomJoseph | Thanks for the comment. I was thinking of equations like porous medium equation by degenerate. | |
| Jul 8, 2014 at 16:55 | comment | added | Chih-Wei Chen | What do you mean by "degenerate"? the coefficient of Laplacian vanishes somewhere on the manifold? If it does, then by using standard method, one can only derive interior estimate (for each $t$), namely, $L^p(\Omega)$ for $\Omega$ compactly contained in the regular portion. In particular, the bound will depend on the distance between degenerate points and the set $\Omega$. | |
| Jul 1, 2014 at 20:54 | review | First posts | |||
| Jul 1, 2014 at 21:14 | |||||
| Jul 1, 2014 at 20:37 | history | asked | TomJoseph | CC BY-SA 3.0 |