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

Abstract

In this paper we study the equation of viscoelasticitywith 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.