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Fourier Sine Transform

  1. Jun 2, 2004 #1
    I'm trying to solve the Laplacian in 2D:
    uxx+uyy=0 in the quarter plane x>0, y>0
    using a Fourier sine transform
    Boundary Conditions:
    u(x,0)=DiracDelta(x-a) , 0< x < infinity and 0< a< infinity
    u(0,y)=0, 0< y < infnity

    I transformed the PDE in x using the definition of the transform with squareroot(2/Pi) in front of the integral transform and got:
    Uyy-k^2*U=0
    hence,
    U=SquareRoot(2/Pi)*Sin(k*a)*Exp(-k*y) Is this correct?
    and how do I inverse sine transform this U(k,y) to get u(x,y)

    Any help please?
     
  2. jcsd
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