Existence and stability results of nonlinear swelling equations with logarithmic source terms

Mohammad Kafini; Mohammad M. Al-Gharabli; Adel M. Al-Mahdi; Mohammad Kafini; Mohammad M. Al-Gharabli; Adel M. Al-Mahdi

doi:10.3934/math.2024627

AIMS Mathematics

2024, Volume 9, Issue 5: 12825-12851. doi: 10.3934/math.2024627

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Research article

Existence and stability results of nonlinear swelling equations with logarithmic source terms

1.
Department of Mathematics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
2.
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received: 13 January 2024 Revised: 11 March 2024 Accepted: 19 March 2024 Published: 03 April 2024
MSC : 35B40, 93D20

We considered a swelling porous-elastic system characterized by two nonlinear variable exponent damping and logarithmic source terms. Employing the Faedo-Galerkin method, we established the local existence of weak solutions under suitable assumptions on the variable exponents functions. Furthermore, we proved the global existence utilizing the well-depth method. Finally, we established several decay results by employing the multiplier method and the Logarithmic Sobolev inequality. To the best of our knowledge, this represents the first study addressing swelling systems with logarithmic source terms.
- swelling system,
- Faedo-Galerkin method,
- well-depth method,
- logarithmic Sobolev inequality,
- variable exponents,
- general decay
Citation: Mohammad Kafini, Mohammad M. Al-Gharabli, Adel M. Al-Mahdi. Existence and stability results of nonlinear swelling equations with logarithmic source terms[J]. AIMS Mathematics, 2024, 9(5): 12825-12851. doi: 10.3934/math.2024627

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Abstract

We considered a swelling porous-elastic system characterized by two nonlinear variable exponent damping and logarithmic source terms. Employing the Faedo-Galerkin method, we established the local existence of weak solutions under suitable assumptions on the variable exponents functions. Furthermore, we proved the global existence utilizing the well-depth method. Finally, we established several decay results by employing the multiplier method and the Logarithmic Sobolev inequality. To the best of our knowledge, this represents the first study addressing swelling systems with logarithmic source terms.

References

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