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Energy decay analysis for Porous elastic system with microtemperature: Classical vs second spectrum approach

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Abstract

The stability features of the dissipative porous elastic systems have piqued the interest of several researchers. The desired exponential decay property of the energy is obtained unless the nonphysical equal speed condition is imposed. This work analyzes the porous elastic system with micro-temperature. First, the exponential stability is obtained in case where there is an assumption on physical constants. Then from a second-spectrum viewpoint, the system’s global well-posedness is proved using the Faedo–Galerkin method. Later, we prove that the microtemperature effect is enough to get the exponential stability of the solution without any assumption on the physical constants. A numerical scheme is introduced. Finally, we present some numerical results which demonstrates the exponential behavior of the solution.

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Acknowledgment

The authors would like to thank the anonymous referees for valuable remarks, suggestions, and careful reading

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, Lebanon

    Hamza Zougheib, Toufic El Arwadi & Mohammad El-Hindi

  2. Department of Mathematics, College of Science, University of Sharjah, P.O.Box 27272, Ash Shariqah, UAE

    Abdelaziz Soufyane

Authors
  1. Hamza Zougheib
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  2. Toufic El Arwadi
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  3. Mohammad El-Hindi
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  4. Abdelaziz Soufyane
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Correspondence to Toufic El Arwadi.

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The manuscript belongs to Theory of PDEs editor by Eduardo Teixeira.

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Zougheib, H., Arwadi, T.E., El-Hindi, M. et al. Energy decay analysis for Porous elastic system with microtemperature: Classical vs second spectrum approach. Partial Differ. Equ. Appl. 5, 6 (2024). https://doi.org/10.1007/s42985-024-00273-3

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  • DOI: https://doi.org/10.1007/s42985-024-00273-3

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