1Department of Applied Mathematics, Zhejiang University, Hangzhou, 310027, China. Supported partially by the National Key Project of China and by the NSFC grants 69874034 2Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812, USA 3Institut 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
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.
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/}
}
TY - JOUR
AU - Kangsheng Liu
AU - Zhuangyi Liu
AU - Bopeng Rao
TI - On an abstract linear elastic system with indefinite damping
JO - ESAIM. Proceedings
PY - 2000
SP - 107
EP - 117
VL - 8
UR - http://geodesic.mathdoc.fr/articles/10.1051/proc:2000008/
DO - 10.1051/proc:2000008
LA - en
ID - EP_2000_8_a7
ER -
%0 Journal Article
%A Kangsheng Liu
%A Zhuangyi Liu
%A Bopeng Rao
%T On an abstract linear elastic system with indefinite damping
%J ESAIM. Proceedings
%D 2000
%P 107-117
%V 8
%U http://geodesic.mathdoc.fr/articles/10.1051/proc:2000008/
%R 10.1051/proc:2000008
%G en
%F EP_2000_8_a7
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
