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.

Voir la notice de l'article provenant de 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.
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},
     publisher = {mathdoc},
     volume = {8},
     year = {2000},
     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
PB  - mathdoc
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
%I mathdoc
%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. http://geodesic.mathdoc.fr/articles/10.1051/proc:2000008/

Cité par Sources :