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

Abstract

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.