A General Stability Result for Viscoelastic Equations with Singular Kernels

Abstract

Viscoelasticity with regular relaxation functions has attracted the attention of many researchers over the last half century or so. Several results concerning existence and long-time behavior of solutions have been established. In particular the exponential, polynomial decay and recently what so called the general decay have been proved. For viscoelasticity, with singular kernels, less attention has been given and few results of existence and exponential decay have been established. In this paper we extend the general decay result, established for regularkernel viscoelasticity, to that with singular kernels. We also present some numerical test to illustrate our theoretical result.