Laplace equation with gradient boundary conditions

*To*: mathgroup at smc.vnet.net*Subject*: [mg123247] Laplace equation with gradient boundary conditions*From*: Tom Wolander <ultimni at hotmail.com>*Date*: Tue, 29 Nov 2011 07:03:46 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

I have bought Mathematica 8 a week ago and this is my first post on this board. My main purpose for the purchase was to work on PDEs, specifically on the heat equation. As one of the first tests I wanted to solve a steady state temperaure distribution on a rectangular domain with a radiative boundary condition on one face (flux=0 on the other 3). I made sure to have continuity in corners. This is a rather easy exercice of a radiating wall - I have solved many of similar and more complex problems "by hand" many years ago. Unfortunately I failed with NDSolve in Mathematica and the tutorials are of no help despite some 4 hours I spent in there. I found only one rather esotherical hint somewhere deep in one "Issue" section on a command which seemed to say that NDSolve could work only with Cauchy boundary conditions. If this were true, then use of Mathematica 8 would be excluded for virtually any work in thermics where the boundary conditions are always of the (non Cauchy) convection/radiation type. In other words the elementary steady state problem (Laplace equation) with flux conditions on boundaries can't be solved? It might be that this issue has been already discussed but I couldn't find a relevant thread by using search. Could somebody help me by answering whether Laplace equation with Robin like BC can't really be solved? And if it can be done, what have I missed to make NDSolve work?

**Follow-Ups**:**Re: Laplace equation with gradient boundary conditions***From:*Mark McClure <mcmcclur@unca.edu>

**Re: Laplace equation with gradient boundary conditions***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>