New general decay of solutions in a porous-thermoelastic system with infinite memory

Abstract

This work is concerned with a one-dimensional thermoelastic porous system with infinite memory effect. We show that the stability of the system holds for a much larger class of kernels than the ones considered in the literature such as the one in [19] and [21]. More precisely, we consider the kernel g:[0,+∞)→(0,+∞) satisfyingg′(t)≤−γ(t)G(g(t)), where γ and G are functions satisfying some specific properties. Under this very general assumption on the behavior of g at infinity, we establish a relation between the decay rate of the solutions and the growth of g at infinity. This work generalizes and improves earlier results in the literature. Moreover, we drop the boundedness assumptions on the history data.