Geodesic
On an abstract linear elastic system with indefinite damping
Kangsheng Liu1 ; Zhuangyi Liu2 ; 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
ESAIM. Proceedings, Tome 8 (2000), pp. 107-117 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/proc:2000008

Kangsheng Liu 1 ; Zhuangyi Liu 2 ; Bopeng Rao 3

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 
@article{EP_2000_8_a7,
     author = {Kangsheng Liu and Zhuangyi Liu and Bopeng Rao},
     title = {On an abstract linear elastic system with indefinite damping},
     journal = {ESAIM. Proceedings},
     pages = {107--117},
     year = {2000},
     volume = {8},
     doi = {10.1051/proc:2000008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2000008/}
}
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Kangsheng Liu; Zhuangyi Liu; Bopeng Rao. On an abstract linear elastic system with indefinite damping. ESAIM. Proceedings, Tome 8 (2000), pp. 107-117. doi: 10.1051/proc:2000008

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