Well-posedness and uniform decay rates for the Klein–Gordon equation with damping term and acoustic boundary conditions

Abstract

In this paper, we consider the Klein–Gordon equation u″+−αΔu+β|u′|pu′+γ|u|qu=0 with damping term and acoustic boundary conditions. This work is devoted to prove the existence of global solutions and uniform decay rates of solutions of the Klein–Gordon equation with damping term and acoustic boundary conditions.