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Help with Poisson equation

  1. May 23, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi, I am looking for a hint, how to solve the following Dirichlet problem. All the standard textbooks have only examples for Dirichlet problems in rectangular or polar coordinate systems, but this problem is defined for a parabolic region.

    2. Relevant equations
    uxx+uyy=2, x>y2
    u(x,y)=0, x=y2

    3. The attempt at a solution
    Transformation into parabolic coordinates and using separation of variables? I am having a problem even with that. The parabolic coordinates with the parabolic Laplacian are here http://eom.springer.de/P/p071170.htm. I don´t even know, how to transform the boundaries. The parabolic coordinates are so unusual. Is this a right method or would you solve it differently? (with Green functions, or Laplace transform etc)
     
  2. jcsd
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