Well-posedness and exponential stability of swelling porous with Gurtin–Pipkin thermoelasticity and delay term

This work examines the exponential stability and well-posedness of a swelling porous system with the Gurtin-Pipkin thermal effect as the sole source of damping over time. We use an essential corollary to the Lumer–Phillips Theorem to demonstrate the well-posedness result under appropriate delay term weight assumptions. Furthermore Using an appropriate Lyapunov functional leads to exponential stability without relying on wave speed assumptions.