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How to solve the screened poisson Equation in 2D?

allyouneedispop
in Analysis and Calculus

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Hi,

I am trying hard to solve the screened poisson equation in 2D for u(x,y):

 

\nabla^2 u(x,y) - u(x,y) =f(x,y) with f(x,y)=exp(-(x^2+y^2)) and

u(x,y)=0 for x,y -> infinity.

 

Could anybody know what is the analytical solution of this equation?

 

I would really thank who could give me any clue about it.

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