Abstract

This paper is concerned with the study of decay rates of the energy associated to 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. Under quite weak assumptions on this measure, we show the decay rates of the semilinear system are described by solutions to a first order nonlinear, dissipative ODE, which recovering and extending some of the results from the literature. The method we used are energy multiplier methods, geometric analysis and a standard integral inequality.