Timeline for Reference Request: Spatially inhomogeneous solutions to parabolic PDE with homogeneous initial data
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2013 at 12:29 | vote | accept | JCM | ||
| Jul 23, 2013 at 11:55 | answer | added | Willie Wong | timeline score: 2 | |
| Jul 23, 2013 at 11:54 | history | edited | JCM | CC BY-SA 3.0 |
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| Jul 23, 2013 at 11:42 | history | edited | JCM | CC BY-SA 3.0 |
see second paragraph.
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| Jul 23, 2013 at 11:05 | comment | added | JCM | I ask again though, can anybody send me a reference to a similar piece of work! I already know how it is done, I just want a piece of work to reference in the introduction of the paper. | |
| Jul 23, 2013 at 11:04 | comment | added | JCM | At Willie, not that low. It is continuous, but obviously not Lipschitz as then a uniqueness result would hold. | |
| Jul 23, 2013 at 11:03 | comment | added | JCM | Sorry Michael Renardy, quite simply, consider a problem which has non-unique solutions to begin with (which I hope is relatively trivial for you). You are correct in that is the starting point though and non-uniqueness must occur to get spatial inhomogeneity. When it is all written up nicely I'll send you a copy. | |
| Jul 23, 2013 at 9:50 | comment | added | Willie Wong | Do you choose $f$ to have particularly low regularity? | |
| Jul 22, 2013 at 19:01 | comment | added | Michael Renardy | You cannot have spatially inhomogeneous solutions if you have uniqueness, because any translate of a solution is also a solution. Since uniqueness holds under quite mild assumptions, I doubt your claim that you have constructed spatially inhomogeneous solutions. At least you should explain more about how this is possible and what is different from "standard" situations. | |
| Jul 22, 2013 at 18:04 | answer | added | Deane Yang | timeline score: 0 | |
| Jul 22, 2013 at 15:28 | comment | added | JCM | Sorry, I intended to only have the nonlinear term depending on $u$ (I suppose that it could depend on $t$ too, but most certainly not on $x$). | |
| Jul 22, 2013 at 15:26 | history | edited | JCM | CC BY-SA 3.0 |
Sorry, I am interested in nonlinear terms which only depend on $u$.
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| Jul 22, 2013 at 14:19 | history | edited | JCM | CC BY-SA 3.0 |
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| Jul 22, 2013 at 14:08 | comment | added | JCM | with $n=1$ yes. | |
| Jul 22, 2013 at 14:04 | comment | added | Deane Yang | Is $\Delta$ the standard Laplacian on $\mathbb{R}$? | |
| Jul 22, 2013 at 14:03 | history | edited | JCM | CC BY-SA 3.0 |
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| Jul 22, 2013 at 13:28 | history | asked | JCM | CC BY-SA 3.0 |