Carlos Nonato, Abbes Benaissa, Anderson Ramos, Carlos Raposo, Mirelson Freitas
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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 strong stability is proved by using general criteria due to Arendt–Batty. Polynomial stability result is obtained by applying the Borichev–Tomilov theorem.
期刊介绍：
Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.
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