Decay of solutions of non-homogenous hyperbolic equations

Abstract

We consider conditions for the decay in time of solutions of non-homogenous hyperbolic equations. It is proven that solutions of the equations go to $0$ in $L^2$ at infinity if and only if an equation's right-hand side uniquely determines the initial conditions in a certain way. We also obtain that a hyperbolic equation has a unique solution that fades when $t\to\infty$.