Timeline for Solutions to Heat Equations with Obstacles!
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2012 at 0:23 | comment | added | Sajjad Lakzian | There is an issue though. Using the implicit function theorem, I get a solution on an open subset of M ...... | |
| Jul 19, 2012 at 16:18 | comment | added | Sajjad Lakzian | Dear George, Thanks for the comment, very helpful. If I let $A(x,t,u) = (u_t + \Delta u)^2 + (\Delta u (p) - \Delta \psi(p))^2 + (u(p) - \psi(p))$ and apply the implicit function theorem to $A = 0$ on an appropriate domain namely, $u(x,t) \le \psi(x)+ \lambda(d(x,p))$ where $\lambda$ is a nonnegative function and $\lambda(0)=0$. Appreciate your help. | |
| Jul 19, 2012 at 10:13 | comment | added | George Lowther | If $t_0$ is arbitrarily small then you can do this by the implicit function theorem. | |
| Jul 18, 2012 at 22:43 | answer | added | timur | timeline score: 2 | |
| Jul 18, 2012 at 13:51 | comment | added | Sajjad Lakzian | Thanks for comment. I fixed some of the conditions, hope my question makes sense now. by the way u is not positive necessarily. I want at some positive time t_0 the graph of |u| to lie under ψ, touching it at a chosen point p with Δu(p)=Δψ(p) or Δu(p)=−Δψ(p) depending on the sign of u near p. | |
| Jul 18, 2012 at 13:50 | history | edited | Sajjad Lakzian | CC BY-SA 3.0 |
added 2 characters in body; added 2 characters in body
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| Jul 18, 2012 at 13:38 | history | edited | Sajjad Lakzian | CC BY-SA 3.0 |
edited body
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| Jul 18, 2012 at 7:44 | comment | added | Anton Petrunin | Please correct the conditions on $u$. At the moment the condition with RHS $\psi(p)$ contradicts the one with RHS $\Delta\psi(p)$. It is not clear what did you want to say... | |
| Jul 18, 2012 at 0:21 | history | asked | Sajjad Lakzian | CC BY-SA 3.0 |