Exponential stabilization of variable coefficient wave equations in a generic tree with small time-delays in the nodal feedbacks

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Guo, Yanni²  Chen, Yunlan¹  Xu, Genqi¹  Zhang, Yaxuan² 

[1] Tianjin Univ, Dept Math, Tianjin 300072, Peoples R China

[2] Civil Aviat Univ China, Inst Appl Math, Sch Sci, Tianjin 300300, Peoples R China

关键词: Generic tree network;    Wave equations;    Variable coefficients;    Time delay;    Exponential stability;   

DOI  :  10.1016/j.jmaa.2012.05.079

来源: Elsevier

【 摘 要 】

In this paper, we study the stability of a general tree network of variable coefficient wave equations with a small delay term in the nodal feedbacks. Using the Lax-Milgram theorem and Co-semigroup theory, we obtain the well-posedness of the system. By a detailed spectral analysis, we show that the spectrum of the system operator distributes in a strip parallel to the imaginary axis under certain conditions. Furthermore, we prove that there is a sequence of (generalized) eigenfunctions that forms a Riesz basis with parenthesis for the energy state space. As a consequence, we obtain the exponential stabilization of the closed-loop system under certain conditions. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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