On Decay of Solutions for a System of Coupled Viscoelastic Equations

Abstract

In this paper, we consider a system of two viscoelastic equations with Dirichlet boundary conditions. For certain class of relaxation functions and initial data, we establish general and optimal decay results. This result extends earlier one of Liu (Nonlinear Anal. TMA 71:2257–2267, 2010), in which only the usual exponential and polynomial decay rates are considered. The conditions of the relaxation functions $g_{1}(t)$ and $g_{2}(t)$ in our work appeared first in Messaoudi and Khulaifi (Appl. Math. Lett. 66:16–22, 2017).