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A pde question that contains fourier series

  1. Jan 7, 2012 #1
    i have been trying to solve a pde problem for 3 days but i couldn't even find the answer,now i feel i m about to have a mental disease,anyone can help me ?


    the question is

    u(x,0) = x

    u(x,2) = 0

    u(0,y) = 0

    d u(1,y) / dx = 0



    [ d^2 u / dx^2 ] + [ d^2 u / dy^2 ] = 0




    i will really be appreciate if someone help me,for long time i have been working on this



    p.s. i have tried for k > 0 and k < 0 but couldnt find anything,the only thing about what happens when k = 0 is we obtain linear equations like F(x) = Ax + B and G(y) = Cy + D,but i have no idea what i wil do in fourier series with these
     
    Last edited: Jan 7, 2012
  2. jcsd
  3. Jan 10, 2012 #2

    LCKurtz

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    If ##U(x,y) = X(x)Y(y)## your X eigenvalue problem becomes$$
    X'' - \lambda X = 0, X(0) = 0, X'(1) = 0$$If you let ##\lambda = -\mu^2##, you should find nonzero eigenvalues.
     
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