Polynomial decay of a internal nonlinear damping structurally acoustic models with variable coefficients

Abstract

In this paper we derive an energy decay estimate of the wave equation with variable coefficients and acoustic boundary condition in a bounded domain under some certain conditions. Our system includes a nonlinear internal damping term, under some checkable conditions on the coefficients, the polynomial decay rate is obtained by the compactness-uniqueness theorem and the Riemannian geometry method.