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On the stability of the swelling porous elastic soils with fluid saturation and Gurtin–Pipkin thermal law

Annali dell'Universita di Ferrara, ISSN: 1827-1510, Vol: 70, Issue: 2, Page: 493-514
2024
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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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