On the exponential decay of a thermoelastic porous system with a forcing term and constant delay

Abstract

In this paper, we consider a one-dimensional porous-elastic system with a forcing and delay terms acting on the porous equations. Under suitable assumptions on the forcing function, we prove that the system is well-posed
by using the semigroups method, and show, depending on the parameters of the system, that the dissipation induced by the heat is strong enough to obtain an exponential stability in the presence of a "small" delay.