Stabilization of the Wave Equation with Localized Nonlinear Damping

We prove some decay estimates of the energy of the wave equation in a bounded domain. The damping is nonlinear and is effective only in a neighborhood of a suitable subset of the boundary. The method of proof is direct and is based on the multipliers technique, on some integral inequalities due to Haraux and Komornik, and on a judicious idea of Conrad and Rao.