|March 14, 2006, 13:21||
Analytical solution to the quarter five problem
I am a PhD student in Applied maths and I am looking forward to solve the elliptic problem: find u(x,y) such that:
-grad(K(grad(u))=dirac(0,0) on Omega=[0,1]*[0,1]; du/dn=0 on Omega\(0,0) : Neumann Boundary Conditions; u(0,0)=1.0 : Dirichlet BCS;
K is a 2*2 tensor.
The question is : How to prove the existence and uniqueness of a solution (L2?)? and what is the analytical solution to the problem?
Usually when there are both neumann and dirichlet conditions together, numerical methods are used. I couldn t find an analytical framwork which deals with this kind of problems. Most of the literature assuming in most cases that the right side is at least continuous and the boundaries are assumed to have a non zero measure.
I would be grateful for your comments and for any indications.
Thank you. Sadek
|Thread||Thread Starter||Forum||Replies||Last Post|
|Problem with hypersonic blunt cone solution||Bharath Hebbal||FLUENT||0||February 15, 2008 03:07|
|asymmetric solution generated by symmetric problem||Twiti||CFX||7||October 16, 2004 20:12|
|Can sb know the analytical solution for 2d unstead||ppaitt||Main CFD Forum||2||September 20, 2004 05:04|
|CFL Condition||Matt Umbel||Main CFD Forum||14||January 12, 2001 15:34|
|Analytical solution to the 3d Laplace equation||Chrys Correa||Main CFD Forum||4||September 11, 2000 19:50|