Question: Hi, it is about partial differential equations 1. Be the problema Utt (x, t) - Au(x, t) = F(x, t), X ER3, tER, u(x, 0)

Hi, it is about partial differential equations

1. Be the problema Utt (x, t) - Au(x, t) = F(x, t), X ER3, tER, u(x, 0) = f(x), XERS, ut (x, 0) = g(x), XER3. Calculate the energy. Suppose that f = 0, g 2 0 y F 2 0. What can you say about the solution u? 2. Study the solution of the following problem by D'Alambert's formula and determine the points where the solution is not C2 . Utt - Uxx = 0, X ER, t ER, u(x, 0) = 10' x>0 x

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