Porous Elastic Soils with Fluid Saturation and Boundary Dissipation of Fractional Derivative Type

This paper deals with a one-dimensional system in the linear isothermal theory of swelling porous elastic soils subject to fractional derivative-type boundary damping. We apply the semigroup theory. We prove well-posedness by the Lumer–Phillips theorem. We show the lack of exponential stability and...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024-04, Vol.23 (2), Article 79
Main Authors: Nonato, Carlos, Benaissa, Abbes, Ramos, Anderson, Raposo, Carlos, Freitas, Mirelson
Format: Article
Language:English
Subjects:
Boundary damping
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Polynomials
Soil porosity
Soil swelling
Soils
Stability
Theorems
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Summary:This paper deals with a one-dimensional system in the linear isothermal theory of swelling porous elastic soils subject to fractional derivative-type boundary damping. We apply the semigroup theory. We prove well-posedness by the Lumer–Phillips theorem. We show the lack of exponential stability and strong stability is proved by using general criteria due to Arendt–Batty. Polynomial stability result is obtained by applying the Borichev–Tomilov theorem.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-023-00937-2