Energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions

Abstract

In this paper we consider the energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions. Motivated by results of Gerbi and Said-houari (2011, 2008), Li and Zhao (2011), Liu and Chen (2016), Wu et al. (2010) and Lu et al. (2011) we intend to study the energy decay rates for problem (1.1)–(1.6). By using the perturbed energy method and Riemannian geometry method, we obtained general energy decay rates