Polynomial stability of the Timoshenko system by one boundary damping

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Bassam, Maya²  Mercier, Denis³  Nicaise, Serge³  Wehbe, Ali^4,1 

[1] Univ Libanaise, EDST, Equipe EDP AN, Hadath, Beyrouth, Lebanon

[2] Univ Valenciennes & Hainaut Cambresis, F-59313 Valenciennes 9, France

[3] Univ Valenciennes & Hainaut Cambresis, FR CNRS 2956, Inst Sci & Tech, LAMAV, F-59313 Valenciennes 9, France

[4] Univ Libanaise, Fac Sci 1, Hadath, Beyrouth, Lebanon

关键词: Timoshenko system;    Boundary feedback;    Non-uniform stability;    Polynomial stability;    Frequency domain conditions;   

DOI  :  10.1016/j.jmaa.2014.12.055

来源: Elsevier

【 摘 要 】

In this paper, we study the indirect boundary stabilization of the Timoshenko system with only one dissipation law. This system, which models the dynamics of a beam, is a hyperbolic system with two wave speeds. Assuming that the wave speeds are equal, we prove non-uniform stability and an optimal polynomial energy decay rate is obtained. Otherwise, if the ratio of the wave speeds is a rational number, we show that the decay rate is of polynomial type. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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