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November 20th, 2014, 05:55 AM  #1 
Newbie Joined: Nov 2014 From: London Posts: 3 Thanks: 0  Poisson equation with three boundary conditions
I have the following 2D Poisson equation (which can also be transformed to Laplace) defined on a triangular region (refer to plot): \begin{equation} \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}=C\end{equation} with the following three boundary conditions: \begin{equation} \frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=0\end{equation} \begin{equation} u=0\,\,\,\,\,\,\,\mathrm{at}\, y=ax+b\end{equation} \begin{equation} c\frac{\partial u}{\partial x}+d\frac{\partial u}{\partial y}=0\,\,\,\,\,\,\,\mathrm{at}\, y=ex+f\end{equation} where $C,a,b,c,d,e,f$ are constants. What is the easiest way to solve this problem (preferably analytically)? 

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boundary, conditions, equation, poisson 
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