I'm trying to solve the Laplacian in 2D:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Fourier Sine Transform

Can you offer guidance or do you also need help?

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