Volume 8, 2000Contrôle des systèmes gouvernés par des équations aux dérivées partielles
|Page(s)||107 - 117|
|Published online||15 August 2002|
On an abstract linear elastic system with indefinite damping
Department of Applied Mathematics, Zhejiang University, Hangzhou, 310027, China. Supported partially by the National Key Project of China and by the NSFC grants 69874034
2 Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812, USA
3 Institut de Recherche Mathématique Avancée, Université de Loius Pasteur de Strasbourg, 7 Rue René-Descartes, 67084 Strasbourg Cedex, France
In this paper we consider an abstract linear system with perturbation of the form (dy/dt) = Ay + εBy on a Hilbert space H, where A is skew-adjoint, B is bounded, and ε is a positive parameter. Motivated by a result of Freitas and Zuazua on the one-dimensional wave equation with indefinite viscous damping [JDE, 1996], we obtain sufficient conditions for the exponential stability for the above system when B is not a dissipative operator. Our result is then applied to many elastic systems with indefinite viscous damping.
© EDP Sciences, ESAIM, 2000
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