Global existence uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation

In this paper, we consider the nonlinear viscoelastic wave equation utt−Δu+∫0th(t−τ)div[a(x)∇u(τ)]dτ+|u|γu=0 with boundary dissipation. Under suitable conditions on the initial data and the relaxation function, we prove the existence and uniqueness of its global solution by means of the Galerkin method and show the uniform decay rate of the energy.