Timeline for Existence of solution for Poisson problem with pure Neumann BCs
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Sep 4, 2019 at 13:32 | answer | added | Antonio Orlando | timeline score: 3 | |
| May 10, 2011 at 2:28 | comment | added | Nilima Nigam | The PDE text by Evans has a good, fairly introductory discussion for elliptic equations of this kind. For a 'reasonable' domain and consistent discretization, your FD method should converge for this problem. | |
| Jan 15, 2011 at 14:06 | comment | added | Willie Wong | Assuming you are dealing with classical solutions, the difference $q' = q_1 - q_2$ of two solutions solves the homogeneous Neumann problem $-\triangle q' + \beta q' = 0$ with 0 Neumann condition. Now use the strong maximum principle and Hopf lemma. | |
| Jan 15, 2011 at 5:14 | comment | added | Mihai | yes the $\beta$ parameter should not be in front of the laplacian. thanks for pointing that out. | |
| Jan 15, 2011 at 5:13 | history | edited | Mihai | CC BY-SA 2.5 |
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| Jan 11, 2011 at 22:25 | comment | added | Harald Hanche-Olsen | A couple remarks: The β parameter is redundant, as you can divide by it and absorb it into $f$. Or did you not intend the β in front of the Laplacian? Also, this being a linear system, the right hand side has no bearing on the uniqueness of any solution. If the homogeneous system has a non-zero solution, then solutions are not unique (if they exist). Finally, you can gain some insight from looking at the one-dimensional case, with Ω an interval. At least it should tell you what to expect. | |
| Jan 11, 2011 at 15:35 | comment | added | Mihai | This is not homework :) My question stems from a finite-difference discretization of such a PDE problem that seems to have trouble converging to a solution upon mesh refinement. If you cannot give the answer out right, could you point me to a reference that discusses this particular form of the equation? I have not been able to find a discussion of this case in the literature, and my experience with theoretical PDE analysis is limited at best, that is, I am not so familiar with standard PDE solution existence proofs. | |
| Jan 11, 2011 at 15:30 | comment | added | Denis Serre | This is homework. Not suitable for MO. | |
| Jan 11, 2011 at 15:28 | history | asked | Mihai | CC BY-SA 2.5 |