Texts: Explanation step by step
Find the unique solution of the following wave equation: u - uxx = 0, x ∈ R, t > 0; ux,0 = x^2 - x; ux,0 = x. (-)
Find the value of the solution at the point (x, t) = ?
Solution:
By Alembert's Formula, the unique solution of * is
u(x, t) = 1/2 * [x^2 - x + x + t + x - t]
u(x, t) = 1/2 * [x^2 + 2xt - t]
The value of the solution at the point (x, t) = ? is 3√(99) + 1 = -2 + √(48.36) + 18
45 49 96 96