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

In this paper we study the equation of viscoelasticityutt−uxxt−F(ux)x=f(x,t)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)f(x,t), that is, they have the same exponential decay or algebraic decay for the case F(s)=s+|s|α−2F(s)=s+|s|α−2(α⩾2)(α⩾2), and for the case F(s)=|s|α−2F(s)=|s|α−2(α>2)(α>2), they have the same algebraic decay.