ON MODELING AND UNIFORM STABILITY OF A PARTIALLY DISSIPATIVE VISCOELASTIC TIMOSHENKO SYSTEM

被引：25

作者：

Alves, Michele O. ^{[1
]}

Gomes Tavares, Eduardo H. ^{[2
]}

Jorge Silva, Marcio A. ^{[3
]}

Rodrigues, Jose H. ^{[1
]}

机构：

[1] Univ Estadual Londrina, Dept Math, BR-86057970 Londrina, PR, Brazil

[2] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP, Brazil

[3] Univ Estadual Londrina, Dept Math, BR-86057970 Londrina, PR, Brazil

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 06期

关键词：

Timoshenko systems; viscoelasticity; stability; decay rates; equal wave speeds; ENERGY DECAY; MEMORY; EQUATION; BEHAVIOR;

D O I：

10.1137/18M1191774

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we first explore the deduction of the mathematical model for some viscoelastic Timoshenko systems. As a consequence, a new partially dissipative viscoelastic Timoshenko system arises with damping mechanism acting only on the shear force. Then, we prove uniform decay rates for this new system with the help of a modern observability inequality, where the assumption of equal speeds of wave propagation is regarded as a sufficient condition. Moreover, we prove that equal wave speeds is also a necessary condition to establish uniform decay rates.

引用

页码：4520 / 4543

页数：24

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