Stability for semilinear wave equation of variable coefficients with acoustic boundary conditions and general boundary memory feedback

Abstract

In this paper, we consider a semilinear wave equation with variable coefficients in a smooth domain, subject to acoustic boundary conditions and dissipative boundary memory feedback, where a general Borel measure is involved. We show that the decay rates of the energy associated to the semilinear systems are given implicitly as solutions of a first order nonlinear, dissipative ODE, which recovers and extends some of the results from the literature. To prove the main result we use energy multiplier methods, geometric analysis combined with Lasiecka and Tataru arguments.