On the stabilization of the Timoshenko system by a weak nonlinear dissipation

In this paper we consider the following Timoshenko‐type system: \documentclass{article}\usepackage{amssymb}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document} \[ \left\{\begin{array}{l@{}} \varphi_{tt}-(\varphi_{x}+\psi)_{x}=0,\quad (0,1)\times {\mathbb{R}}_{+}\\ \psi_{tt}-\...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2009-03, Vol.32 (4), p.454-469
Main Authors: Messaoudi, Salim A., Mustafa, Muhammad I.
Format: Article
Language:English
Subjects:
Exact sciences and technology
general decay
Mathematical analysis
Mathematics
Sciences and techniques of general use
Timoshenko
weak dissipation
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Summary:In this paper we consider the following Timoshenko‐type system: \documentclass{article}\usepackage{amssymb}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document} \[ \left\{\begin{array}{l@{}} \varphi_{tt}-(\varphi_{x}+\psi)_{x}=0,\quad (0,1)\times {\mathbb{R}}_{+}\\ \psi_{tt}-\psi_{xx}+\varphi_{x}+\psi +\alpha (t)g(\psi_{t})=0,\quad (0,1)\times {\mathbb{R}}_{+} \end{array} \right. \] \end{document} Without imposing any restrictive growth assumption on g at the origin, we establish a general decay result depending on g and α. Copyright © 2008 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.1047