Energy Decay of Solutions of Porous-Elastic System With Kelvin–Voigt Damping and Infinite Memory
Adel M. Al-Mahdi
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Contribution: Investigation, Formal analysis, Writing - original draft, Visualization, Conceptualization, Methodology, Writing - review & editing
Search for more papers by this authorMohammed Al-Gharabli
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Contribution: Conceptualization, Methodology, Investigation, Visualization, Formal analysis, Supervision, Writing - original draft
Search for more papers by this authorCorresponding Author
Tijani A. Apalara
Department of Mathematics, University of Hafr Al- Batin (UHB), Hafr al-Batin, Saudi Arabia
Correspondence:
Tijani A. Apalara ([email protected])
Contribution: Writing - review & editing, Validation, Visualization, Supervision, Conceptualization, Investigation
Search for more papers by this authorAdel M. Al-Mahdi
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Contribution: Investigation, Formal analysis, Writing - original draft, Visualization, Conceptualization, Methodology, Writing - review & editing
Search for more papers by this authorMohammed Al-Gharabli
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Contribution: Conceptualization, Methodology, Investigation, Visualization, Formal analysis, Supervision, Writing - original draft
Search for more papers by this authorCorresponding Author
Tijani A. Apalara
Department of Mathematics, University of Hafr Al- Batin (UHB), Hafr al-Batin, Saudi Arabia
Correspondence:
Tijani A. Apalara ([email protected])
Contribution: Writing - review & editing, Validation, Visualization, Supervision, Conceptualization, Investigation
Search for more papers by this authorFunding: This work is partially funded by KFUPM grant no. INCB2531.
ABSTRACT
This paper examines a one-dimensional porous-elastic system that incorporates Kelvin–Voigt damping and viscoelastic damping of infinite memory type in the volume fraction equation. We investigate the asymptotic behavior of solutions of the system and establish general energy decay under specific conditions on the relaxation function and the time-dependent coefficient of Kelvin–Voigt damping. Our findings provide valuable insights into the stability features of viscoelastic porous structures and enhance some well-known results in the literature.
Conflicts of Interest
The authors declare no conflicts of interest.
Open Research
Data Availability Statement
The authors have nothing to report.
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