Singular limits of binary mixtures in solids theory

被引：0

作者：

Freitas, M. M. ^{[1
]}

Dos Santos, M. J. ^{[2
]}

Santos, M. L. ^{[3
]}

Ramos, A. J. A. ^{[1
]}

Almeida Jr, D. S. ^{[3
]}

机构：

[1] Fed Univ Para, Fac Math, Raimundo Santana St S-N, BR-68721000 Salinopolis, PA, Brazil

[2] Fed Univ Para, Fac Exact Sci & Technol, Manoel de Abre St S-N, BR-68440000 Abaetetuba, PA, Brazil

[3] Fed Univ Para, PhD Program Math, Augusto Correa St, BR-66075110 Belem, PA, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 526卷 / 01期

关键词：

Binary mixtures; Singularly perturbed systems; Global attractor; Upper semicontinuity; NON-LINEAR DIFFUSION; THERMOVISCOELASTIC MIXTURES; UPPER SEMICONTINUITY; EVOLUTION-EQUATIONS; CONTINUUM THEORIES; EXPONENTIAL DECAY; ATTRACTOR; STABILITY; 2ND-ORDER;

D O I：

10.1016/j.jmaa.2023.127245

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the long-term behavior, as a certain coupling parameter alpha becomes large, of a one-dimensional model of a binary mixture of solids with nonlinear damping and nonlinear feedback forces. We prove the existence of a smooth global attractor with finite fractal dimension and study its limiting properties when alpha tends to infinity. More precisely, we prove that this limit coincides with a one-dimensional single wave equation. Finally, we also prove convergence of the global attractor of the binary mixture model to the global attractor of the single wave equation as alpha -> infinity. To the best of our knowledge, this result is new for singularly perturbed systems of a binary mixture of solids.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：22

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