Local convergence and speed estimates for semilinear wave systems damped by boundary friction

Abstract

We study the local convergence to equilibria, as time goes to infinity, of trajectories of semilinear wave systems with friction damping on the boundary and subject to nonlinear potential energy. Estimates for the speed of convergence are obtained in terms of the behavior of the nonlinear feedback close to the origin. As an example of application, we show that the trajectories of a sine-Gordon system with nonlinear boundary damping, approach equilibria at least polynomially.