Abstract
The present paper is devoted to studying the well-posedness and exponential stability of the one-dimensional system in the linear isothermal theory of swelling porous elastic soils with fluid saturation and Gurtin–Pipkin thermal law. For the well-posedness, we apply the well-known Hille–Yosida theorem of semigroup theory. To prove exponential stability without assuming that the wave speeds are the same, we use the energy method which consists of constructing a Lyapunov functional equivalent to the system’s total energy.
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Funding
A. J. A. Ramos thanks the CNPq for financial support through Grant 310729/2019-0. M. M. Freitas thanks the CNPq for financial support through Grant 313081/2021-2.
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Ramos, A.J.A., Nonato, C.A., Raposo, C.A. et al. On the stability of the swelling porous elastic soils with fluid saturation and Gurtin–Pipkin thermal law. Ann Univ Ferrara 70, 493–514 (2024). https://doi.org/10.1007/s11565-023-00486-1
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DOI: https://doi.org/10.1007/s11565-023-00486-1