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Issue ESAIM: Proc.
Volume 8, 2000
Contrôle des systèmes gouvernés par des équations aux dérivées partielles
Page(s) 107 - 117
DOI http://dx.doi.org/10.1051/proc:2000008

ESAIM: Proc., 2000, Vol. 8, pp. 107-117
DOI: 10.1051/proc:2000008

On an abstract linear elastic system with indefinite damping

Kangsheng Liu1, Zhuangyi Liu2 and Bopeng Rao3

1  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


Abstract
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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