General energy decay estimates for a variable coefficient viscoelastic semilinear wave equation with logarithmic source term and acoustic boundary conditions

Abstract

In this paper, we consider a variable coefficient viscoelastic semilinear wave equation with logarithmic source term and acoustic boundary conditions in domains with non‐locally reacting boundary. By potential well method, we get the global existence of solution and through several important lemmas, we prove the general energy decay estimate of the system.