Decay rate for a class of viscoelasticity equation with nonlinear damping on the boundary

In this paper we study the equation of viscoelasticity utt −uxxt − F(ux )x = f (x, t) with the nonlinear damping term on the boundary. Making use of the so-called energy perturbation method and a comparison inequality we prove the relationship between decay rate of solutions and f (x, t), that is, they have the same exponential decay or algebraic decay for the case F(s) = s + |s|α−2 (α 2), and for the case F(s) = |s|α−2 (α > 2), they have the same algebraic decay. © 2007 Elsevier Inc. All rights reserved.