Stabilizability of systems of one-dimensional wave equations by one internal or boundary control force

Authors
Khodja, FA Bader, A
Citation
Fa. Khodja et A. Bader, Stabilizability of systems of one-dimensional wave equations by one internal or boundary control force, SIAM J CON, 39(6), 2001, pp. 1833-1851
Citations number
12
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN journal
03630129 → ACNP
Volume
39
Issue
6
Year of publication
2001
Pages
1833 - 1851
Database
ISI
SICI code
0363-0129(20010412)39:6<1833:SOSOOW>2.0.ZU;2-7
Abstract
We study the internal and boundary stabilizability of a system of wave equa tions by one control force. We prove that the classical internal damping ap plied to only one of the equations never gives exponential stability if the wave speeds are different and, if the wave speeds are the same, we give ex plicit necessary and sufficient conditions for the stability to occur. We a lso study the simultaneous boundary stabilization of the same system.