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

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 ex...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2023-04, Vol.74 (2), Article 72
Main Authors: Al-Mahdi, A. M., Al-Gharabli, M. M., Kissami, I., Soufyane, A., Zahri, M.
Format: Article
Language:English
Subjects:
Damping
Decay
Elastic systems
Engineering
Mathematical Methods in Physics
Polynomials
Swelling
Theoretical and Applied Mechanics
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Summary: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.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-023-01962-6