Asymptotic behavior for a porous-elastic system with fractional derivative-type internal dissipation

Abstract

This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and establishes the dissipativity property of the system. We use the semigroup theory. The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem. We present two results for the asymptotic behavior: Strong stability of the \(C_0\)-semigroup associated with the system using Arendt-Batty and Lyubich-Vũ’s general criterion and polynomial stability applying Borichev and Tomilov’s Theorem.