General decay of solutions of a viscoelastic equation

Abstract

In this paper we consider the following viscoelastic equation:

$$u_{tt}-\mathrm{\Delta }u+\underset{0}{\overset{t}{\int }}g(t-\tau )\mathrm{\Delta }u(\tau )d\tau =0,$$

in a bounded domain, and establish a general decay result which is not necessarily of exponential or polynomial type. This work generalizes and improves earlier results in the literature.