GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH BALAKRISHNAN-TAYLOR DAMPING

Abstract

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions on the relaxation function and with certain initial data and by adopting the perturbed energy method, we establish uniform decay rate of the solution energy in terms of the behavior of the relaxation function, which are not necessarily of exponential or polynomial decay.