Decay of solutions of the wave equation in a star-shaped domain with nonlinear boundary feedback

Abstract

We study the uniform stabilization of the wave equation by means of a nonlinear dissipative boundary feedback. We consider a Neumann condition on the whole boundary, and the observation is the boundary displacement and velocity. We obtain, in a nonlinear framework, estimates of the decay, for any displacement. We establish a similar result for the one-dimensional wave equation with a variable coefficient.