Formally solve the following boundary value problem

[modeiry88]

Homework Statement

Formally solve the following boundary value problem using Fourier Transforms.

Homework Equations

($$\partial$$$$^{2}$$u/$$\partial$$x$$^{2}$$)+($$\partial$$$$^{2}$$u/$$\partial$$y$$^{2}$$) = 0

(-$$\infty$$<x<$$\infty$$,0<y<1)

u(x,0)= exp$$^{-2|x|}$$

(-$$\infty$$<x<$$\infty$$)

u(x,1)=0


(-$$\infty$$<x<$$\infty$$)

u(x,y)$$\rightarrow$$ 0 uniformaly in y as |x| $$\rightarrow$$$$\infty$$

The Attempt at a Solution

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[berkeman]

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