Wilson Oliveira, Sebastião Cordeiro, Carlos Alberto Raposo da Cunha, Octavio Vera
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引用次数: 0
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.
期刊介绍:
Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.