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Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system

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Abstract

In this paper, we consider a one-dimensional thermoelastic porous system with memory effect. We establish the existence and uniqueness result using the Faedo Galerkin approximations method. Then, we prove a general decay result under a very general assumption on the relaxation function and for suitable initial data with enough regularities. In order to validate our theoretical results, we discretize our system using hybrid numerical scheme and we present several numerical experiments and tests.

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Acknowledgements

The authors thank King Fahd University of Petroleum and Minerals (KFUPM) and University of Lille for their continuous support. The authors also thank the referee for his/her valuable comments and corrections which improved a lot this work. This work is supported by KFUPM under project # SB201026.

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Authors and Affiliations

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

    Adel M. Al-Mahdi

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

    Adel M. Al-Mahdi & Mohammad Kafini

  3. Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Mohammad Kafini

  4. Bayero University Kano, Kano, Kano State, Nigeria

    Jamilu Hashim Hassan

  5. Arts et Metiers Institute of Technology, Centrale Lille, Junia, ULR2697 - L2EP, University of Lille, 59000, Lille, France

    Mohamed Alahyane

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  1. Adel M. Al-Mahdi
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  2. Mohammad Kafini
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  3. Jamilu Hashim Hassan
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  4. Mohamed Alahyane
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Correspondence to Adel M. Al-Mahdi.

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Al-Mahdi, A.M., Kafini, M., Hassan, J.H. et al. Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system. Z. Angew. Math. Phys. 73, 94 (2022). https://doi.org/10.1007/s00033-022-01733-9

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  • DOI: https://doi.org/10.1007/s00033-022-01733-9

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