Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

In this paper the nonlinear viscoelastic wave equation in canonical form |u(t)|(rho)u(tt) - (delta)u - (delta)u(tt) + integral(t)(o) g(t - (tau)) (delta) u(tau)d (tau) = b|u|(p-2)u with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set.