Timeline for A comparison principle for parabolic equation
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11 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Apr 22, 2014 at 19:46 | vote | accept | riem | ||
| Apr 21, 2014 at 15:52 | comment | added | leo monsaingeon | So there is a PDE in the end, and you were basically trying to compare a subsolution and a supersolution of your PDE. Your computation must have gone wrong at some point: the weak formulation shouldn't involve time derivatives on the boundary, but only in the interior $\Omega\times(0,T)$ of the parabolic domain. | |
| Apr 21, 2014 at 15:46 | answer | added | leo monsaingeon | timeline score: 2 | |
| Apr 21, 2014 at 14:31 | comment | added | riem | @leomonsaingeon Sorry for late response. There is no PDE so to speak, it's jsut something I thought about. I have heavily changed the question (it's much easier now). | |
| Apr 21, 2014 at 14:30 | history | edited | riem | CC BY-SA 3.0 |
added 162 characters in body; edited title
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| Apr 16, 2014 at 20:36 | comment | added | leo monsaingeon | What is the PDE, then? it seems you have time derivatives on the boundary, which I've never seen before... | |
| Apr 16, 2014 at 19:39 | comment | added | riem | @leomonsaingeon $p$ is negative. Hmm, I guess I should think more carefully about the space $\varphi$ belongs to.. perhaps also $\varphi \in L^2(0,T;H^1(\partial\Omega)) \cap H^{-1}(0,T;L^{2}(\partial\Omega))$. Maybe $\varphi$ should be smooth on the closure. I am just starting with this formulation, i just called it degenerate due to the negative power. | |
| Apr 16, 2014 at 18:21 | comment | added | leo monsaingeon | Is $p\in R$ really negative, or is it just a typo? In which sense do you understand $\varphi '$ (I guess $\partial \varphi/\partial t$) if you only have $\varphi\in \mathcal{C}^1(0,T;L^2(\Omega))$ as a time regularity? Of course with your assumptions you also have $\varphi\in L^{2}(0,T;H^1(\Omega))\hookrightarrow L^{2}(0,T;H^{1/2}(\partial\Omega))\hookrightarrow L^{2}(0,T;L^2(\partial\Omega))$, but this still doesn't make sense of the time derivative on the boundary. I'm a little surprised by your $\partial\Omega$ boundary terms, can you tell us what is your (degenerate) parabolic PDE? | |
| Apr 16, 2014 at 16:41 | review | First posts | |||
| Apr 16, 2014 at 16:41 | |||||
| Apr 16, 2014 at 16:24 | history | asked | riem | CC BY-SA 3.0 |