# Poisson equation with three boundary conditions

1. Nov 20, 2014

### azzaz

I have the following 2D Poisson equation (which can also be transformed

to Laplace) defined on a triangular region (refer to plot):

\frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C

with the following three boundary conditions:

\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=0

u=0\,\,\,\,\,\,\,\mathrm{at}\, y=ax+b

c\frac{\partial u}{\partial x}+d\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=ex+f

where C,a,b,c,d,e,f are constants.

What is the easiest way to solve this problem (preferably analytically)?

View attachment 75674

2. Nov 20, 2014

### ZetaOfThree

Can you use separation of variables?

3. Nov 20, 2014

### SteamKing

Staff Emeritus