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Exponential and polynomial decay results for a swelling porous elastic system with a single nonlinear variable exponent damping: theory and numerics

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Abstract

We consider a swelling porous elastic system with a single nonlinear variable exponent damping. We establish the existence result using the Faedo–Galerkin approximations method, and then, we prove that the system is stable under a natural condition on the parameters of the system and the variable exponent. We obtain exponential and polynomial decay results by using the multiplier method, and these results generalize the existing results in the literature. In addition, we end our paper with some numerical illustrations.

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Acknowledgements

The authors thank King Fahd University of Petroleum and Minerals (KFUPM) and University of Sharjah for their continuous supports. The authors also thank the referees for their valuable comments and corrections which improved a lot this work. This is funded by KFUPM, Grant No. INCB2215.

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Authors and Affiliations

  1. The Preparatory Year Program, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia

    A. M. Al-Mahdi & M. M. Al-Gharabli

  2. The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia

    A. M. Al-Mahdi & M. M. Al-Gharabli

  3. Mohammed VI Polytechnic University, Lot 990 Hay Moulay Rachid, 43150, Benguerir, Morocco

    I. Kissami

  4. Department of Mathematics Research groups MASEP and BioInformatics FG, University of Sharjah Sharjah, Sharjah, United Arab Emirates

    A. Soufyane & M. Zahri

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  1. A. M. Al-Mahdi
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Contributions

AS suggested the model, and AMA-M, MMA-G and AS performed the necessary theory and proofs. IK and MZ performed the numerical and computational part.

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Correspondence to M. Zahri.

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Al-Mahdi, A.M., Al-Gharabli, M.M., Kissami, I. et al. Exponential and polynomial decay results for a swelling porous elastic system with a single nonlinear variable exponent damping: theory and numerics. Z. Angew. Math. Phys. 74, 72 (2023). https://doi.org/10.1007/s00033-023-01962-6

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  • DOI: https://doi.org/10.1007/s00033-023-01962-6

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