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Problem 4. Consider the heat equation in a two-dimensional rectangular region, 0 < x < L, 0 < y < H, ∂u ∂t = k ∂ 2u ∂x2 + ∂ u ∂y2 subject to the initial condition u(x,y,0) = f(x,y). Solve the initial-boundary value problem and analyze the temperature as t → ∞ if the ,
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