Well-Posedness and Exponential Stability of Swelling Porous with Gurtin–Pipkin Thermoelasticity

Tijani Abdul-Aziz Apalara () and Ohud Bulayhan Almutairi
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Tijani Abdul-Aziz Apalara: Department of Mathematics, University of Hafr Al-Batin (UHB), Hafr Al-Batin 31991, Saudi Arabia
Ohud Bulayhan Almutairi: Department of Mathematics, University of Hafr Al-Batin (UHB), Hafr Al-Batin 31991, Saudi Arabia

Mathematics, 2022, vol. 10, issue 23, 1-17

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.

Keywords: swelling porous problem; Gurtin–Pipkin thermal law; exponential stability; well-posedness; energy method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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