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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):


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

    with the following three boundary conditions:


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


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


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    Gold Member

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


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    Your attachment didn't attach.
  5. Nov 20, 2014 #4
    This is the attachment
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