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On a Lord–Shulman swelling porous thermo-elastic soils system with microtemperature effect: well-posedness and stability results

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Abstract

This work investigates the well-posedness and stability outcomes of the one-dimensional Cauchy problem within a system involving swelling-porous elastic soils and thermal effects. The heat conduction in this system is described by the Lord–Shulman theory. By the energy method, we establish the existence of solutions and then prove an exponential stability result under suitable hypotheses. Our results were achieved without the need for the condition of equal velocities, and it is also considered a good improvement to our work in the paper (Choucha et al. in Mathematics 11(23):4785, 2023), completely dispensing with any damping term.

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Acknowledgements

For any decision. the authors are grateful to the anonymous referees for the careful reading and their important observations/suggestions for the sake of improving this paper.

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Authors and Affiliations

  1. Department of Material Sciences, Faculty of Sciences, Amar Teledji Laghouat University, Laghouat, Algeria

    Abdelbaki Choucha

  2. Laboratory of Mathematics and Applied Sciences, Ghardaia University, Bounoura, Algeria

    Abdelbaki Choucha

  3. Department of Mathematics, College of Science, Qassim University, 51452, Buraydah, Saudi Arabia

    Salah Boulaaras

  4. Department of Civil Engineering, College of Engineering, Institute of Energy Infrastructure (IEI), Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000, Kajang, Selangor, Malaysia

    Rashid Jan

Authors
  1. Abdelbaki Choucha
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  2. Salah Boulaaras
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  3. Rashid Jan
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Correspondence to Salah Boulaaras.

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Choucha, A., Boulaaras, S. & Jan, R. On a Lord–Shulman swelling porous thermo-elastic soils system with microtemperature effect: well-posedness and stability results. Afr. Mat. 35, 30 (2024). https://doi.org/10.1007/s13370-024-01170-z

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