Asymptotic stability for non-autonomous damped wave systems

We study the problem of asymptotic stability, as time tends to infinity, of solutions of dissipative wave systems, governed by time-dependent nonlinear damping forces and subject to the action of strongly nonlinear potential energies. In the final part of the paper we also consider the case of polyharmonic wave operators and higher-order dissipation terms. With appropriate choices of the auxiliary function k we obtain a number of useful special cases of Theorems 1 and 2. The linear case and the case when n=1 are treated in detail.