# Fourier Sine Transform

1. Jun 2, 2004

### urista

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)