LOCAL ASYMPTOTIC STABILITY FOR DISSIPATIVE WAVE SYSTEMS

We study the question of asymptotic stability, as time tends to infini ty, of solutions of dissipative wave systems, governed by time-depende nt nonlinear damping forces and by strongly nonlinear potential energi es. This problem had been considered earlier for potential energies wh ich arise from restoring forces, whereas here we allow as well for the effect of amplifying forces. Global asymptotic stability can then no longer be expected, and should be replaced by local stability. The con clusions are related to and supplement earlier work of Payne and Satti nger [7], who treated the nondissipative case, and of Hale [1], who sh owed the existence of connected global attractors.