Exponential energy decay of solutions of viscoelastic wave equations

In this paper we consider the nonlinear viscoelastic equationutt−Δu+∫0tg(t−τ)Δu(τ)dτ+ut=|u|p−1uin Ω×(0,∞), with initial conditions and Dirichlet boundary condition. Under some appropriate assumption on g, by introducing a potential well we establish the global existence result for the equation above. Furthermore, we investigate explicit exponential energy decay of the viscoelastic wave equation under the potential well.