Partial Differential Equations Find a formula for the solution u(x, t) to the fo
ID: 2973383 • Letter: P
Question
Partial Differential Equations Find a formula for the solution u(x, t) to the following problem for the wave equation in a half-line {utt - uxx = 0 for x 0, t 0 ux|x = 0 = 0 for t 0, u|t = 0 = f(x), ut|t = 0 = g(x) for x 0, where f and g are given functions. Hint: Use appropriate extensions of f, g to the whole real line. (b) Let f(x) = 0 for x 1; f(x) = x - 1 for 1 x 2; f(x) = -x + 3 for 2 x 3; f(x) = 0 for x 3. Let also g = 0. Plot the solution of the problem above for t = 3. If you decide to include the graph of f as well, indicate clearly which graph corresponds to u(x, 3).Explanation / Answer
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