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Well-Posedness and Stability Results for Lord Shulman Swelling Porous Thermo-Elastic Soils with Microtemperature and Distributed Delay

Author

Listed:
  • Abdelbaki Choucha

    (Department of Material Sciences, Faculty of Sciences, Amar Teledji Laghouat University, Laghouat 03000, Algeria)

  • Salah Boulaaras

    (Department of Mathematics, College of Sciences and Arts in ArRass, Qassim University, Buraydah 51452, Saudi Arabia)

  • Rashid Jan

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

  • Mohammed AbaOud

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia)

  • Rowaida Alrajhi

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia)

Abstract

The Lord Shulman swelling porous thermo-elastic soil system with the effects of microtemperature, temperatures and distributed delay terms is considered in this study. The well-posedness result is established by the Lumer–Phillips corollary applied to the Hille–Yosida theorem. The exponential stability result is proven by the energy method under suitable assumptions.

Suggested Citation

  • Abdelbaki Choucha & Salah Boulaaras & Rashid Jan & Mohammed AbaOud & Rowaida Alrajhi, 2023. "Well-Posedness and Stability Results for Lord Shulman Swelling Porous Thermo-Elastic Soils with Microtemperature and Distributed Delay," Mathematics, MDPI, vol. 11(23), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4785-:d:1288786
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