Abstract
The focus of this work is to investigate the well-posedness and exponential stability of a swelling porous system with the Gurtin–Pipkin thermal effect as the only source of damping. The well-posedness result is achieved using an essential corollary to the Lumer–Phillips Theorem. By constructing a suitable Lyapunov functional, we establish an exponential stability result without the conventional limitation to the system’s parameters (coined a stability number in the literature). Generally, the study demonstrates that the unique dissipation from the Gurtin–Pipkin thermal law is sufficient to stabilize the system exponentially, irrespective of the system’s parameters.
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