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

Abdelbaki Choucha, Salah Boulaaras (), Rashid Jan, Mohammed AbaOud and Rowaida Alrajhi
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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

Mathematics, 2023, vol. 11, issue 23, 1-18

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.

Keywords: Lord Shulman; mathematical operators; swelling porous system; partial differential equations; general decay; distributed delay term (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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