LAUSR

This work is concerned with a coupled system of viscoelastic wave equations in the presence of infinite-memory terms. We show that the stability of the system holds for a much larger class of kernels. More precisely, we consider the kernels \begin{document}$ g_i : [0, +\infty) \rightarrow (0, +\infty) $\end{document} satisfying \begin{document}$ g_i'(t)\leq-\xi_i(t)H_i(g_i(t)),\qquad\forall\,t\geq0 \quad\mathrm{and\ for\ }i = 1,2, $\end{document} where \begin{document}$ \xi_i $\end{document} and \begin{document}$ H_i $\end{document} are functions satisfying some specific properties. Under this very general assumption on the behavior of \begin{document}$ g_i $\end{document} at infinity, we establish a relation between the decay rate of the solutions and the growth of \begin{document}$ g_i $\end{document} at infinity. This work generalizes and improves earlier results in the literature. Moreover, we drop the boundedness assumptions on the history data, usually made in the literature.