On the Stabilization of a Non-Dissipative Cauchy Viscoelastic Problem

In this paper, we consider a linear Cauchy viscoelastic problem with an external source term. We find the critical weaker conditions on the source \({f(x,t)}\) needed to show that, for any compactly supported initial data and for an exponentially decaying relaxation function, the decay of the first energy of solution is polynomial.