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Poisson equation with three boundary conditions

  1. Nov 20, 2014 #1
    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)?

    View attachment 75674
     
  2. jcsd
  3. Nov 20, 2014 #2

    ZetaOfThree

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    Gold Member

    Can you use separation of variables?
     
  4. Nov 20, 2014 #3

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Your attachment didn't attach.
     
  5. Nov 20, 2014 #4
    This is the attachment
    upload_2014-11-20_18-26-23.png
     
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