Stability results of a swelling porous-elastic system with two nonlinear variable exponent damping

Abdelaziz Soufyane; Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Imad Kissami; Mostafa Zahri; Abdelaziz Soufyane; Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Imad Kissami; Mostafa Zahri

doi:10.3934/nhm.2024019

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 430-455. doi: 10.3934/nhm.2024019

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Stability results of a swelling porous-elastic system with two nonlinear variable exponent damping

1.
Department of Mathematics, College of Sciences, University of Sharjah, P.O.Box 27272, Sharjah, United Arab Emirates
2.
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
3.
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
4.
College of Computing, Mohammed Ⅵ Polytechnic University, Lot 990 Hay Moulay Rachid, Benguerir 43150, Morocco

Received: 07 March 2024 Revised: 25 March 2024 Accepted: 30 March 2024 Published: 09 April 2024

In this paper, a swelling soil system with two nonlinear dampings of variable exponent-type is considered. The stability analysis of this system is investigated and it is proved that the system is stable under a natural condition on the parameters of the system and the variable exponents. It is noticed that one variable damping is enough to achieve polynomial and exponential decay and the decay is not necessarily improved if the system has two variable dampings.
- swelling soil,
- Enemy method,
- asymptotic behavior,
- variable exponents
Citation: Abdelaziz Soufyane, Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Imad Kissami, Mostafa Zahri. Stability results of a swelling porous-elastic system with two nonlinear variable exponent damping[J]. Networks and Heterogeneous Media, 2024, 19(1): 430-455. doi: 10.3934/nhm.2024019

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Abstract

In this paper, a swelling soil system with two nonlinear dampings of variable exponent-type is considered. The stability analysis of this system is investigated and it is proved that the system is stable under a natural condition on the parameters of the system and the variable exponents. It is noticed that one variable damping is enough to achieve polynomial and exponential decay and the decay is not necessarily improved if the system has two variable dampings.

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