Answer to Question #25847 in Differential Equations for Sabrina DelCourt

Question

If u is a solution of the wave equation u_tt - c^2u_xx = 0 on -infinity < x < infinity, t > 0 for which u-->0, u_x-->0, and u_t-->0 as x-->+/-infinity, then the enrgy E = the integral from -infinity to +infinity of
(u^2_t + c^2u^2_x)dx is constant.
Is there a corresponding conserved quantity E* for solutions of the equation u_tt - c^2u_xx - bu = 0?