Exponential energy decay of solutions of viscoelastic wave equations

In this paper we consider the nonlinear viscoelastic equation u(tt) - Delta + integral(t)(0) g(t-tau)Delta u(tau)d tau + u(t) = vertical bar u vertical bar(p-t) u in Omega x (0, infinity), 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. (C) 2008 Elsevier Inc. All rights reserved.