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Use the Fourier transform to find the solution of the following initial boundaryvalue Laplace equations uxx...

Use the Fourier transform to find the solution of the following initial boundaryvalue Laplace equations

uxx + uyy = 0, −∞ < x < ∞ 0 < y < a,

u(x, 0) = f(x), u(x, a) = 0, −∞ < x < ∞

u(x, y) → 0 uniformlyiny as|x| → ∞.

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