Answer to Question #25319 in Differential Equations for Jacob Milne

Question

Suppose u is a solution of the wave equation u_tt - c^2u_xx = 0 on -infinity less than x less than 0, t greater than 0, and suppose that u-->0, u_x-->0, and u_t-->0 as x approaches +/- infinity. Show that E = ∫∞−∞ (u^2_t+c^2u^2_x)dx is constant.