具有分数导数型内耗散的多孔弹性系统的渐近行为

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-02-21 DOI:10.1007/s13540-024-00250-y

Wilson Oliveira, Sebastião Cordeiro, Carlos Alberto Raposo da Cunha, Octavio Vera

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引用次数: 0

摘要

这项研究涉及具有分数导数类型内部阻尼的多孔弹性系统的求解和渐近分析。我们考虑了一个增强模型。提出了能量函数，并确定了系统的耗散特性。我们使用了半群理论。通过应用著名的 Lumer-Phillips 定理，我们得到了解的存在性和唯一性。我们给出了渐近行为的两个结果：与系统相关的 \(C_0\)-semigroup 的强稳定性使用了 Arendt-Batty 和 Lyubich-Vũ's 一般标准，多项式稳定性使用了 Borichev 和 Tomilov 定理。

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

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.

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

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.