5. Let g(t) be a smooth function and u(x, t) be a solution of the following problem: Uų = k?u 0 < x < L,t > 0, u(0, t) = g(t), t > 0, u(L, t) = 0, t > 0, u(r, 0) = f(x), 0 < x < L. Prove u(r, t) decays to 0 if g(t) → 0 as t→ o.

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A: our objective is to find the required derivative

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