Attractors and their structure for semilinear wave equations with nonlinear boundary dissipation

Abstract

Long time behavior of a semilinear wave equation with nonlinear boundary dissipation is considered. It is shown that weak solutions generated by the wave dynamics converge asymptotically to a finite dimensional attractor. It is known [CEL1] that the attractor consists of all full trajectories emanating from the set of stationary points. Under the additional assumption that the set of stationary points is finite it is proved that every solution converges to some stationary points at an exponential rate.