General Energy Decay of Solutions for a Wave Equation with Nonlocal Damping and Nonlinear Boundary Damping

Abstract

In this paper, we consider a nonlinear wave equation with nonlocal damping and nonlinear boundary damping. We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping by using of the multiplier technique from the idea of Martinez [1]. Our result extends and improves the result in the literature such as the work by Lourêdo, Ferreira de Araújo and Mirandain [2] in which only exponential energy decay is considered. Furthermore, we get also the energy decay for the equation with nonlocal damping only but without nonlinear boundary damping.