On a Lord?Shulman swelling porous thermo-elastic soils system with microtemperature effect: well-posedness and stability results
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 exist...
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Springer Science and Business Media Deutschland GmbH
2025
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| Summary: | 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. ? African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2024. |
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