EXPONENTIAL STABILITY OF THE SEMIGROUP ASSOCIATED WITH A THERMOELASTIC SYSTEM

Authors
LIU ZG ZHENG SM
Citation
Zg. Liu et Sm. Zheng, EXPONENTIAL STABILITY OF THE SEMIGROUP ASSOCIATED WITH A THERMOELASTIC SYSTEM, Quarterly of applied mathematics, 51(3), 1993, pp. 535-545
Citations number
14
Categorie Soggetti
Mathematics,Mathematics
Journal title
Quarterly of applied mathematics → ACNP
ISSN journal
0033569X
Volume
51
Issue
3
Year of publication
1993
Pages
535 - 545
Database
ISI
SICI code
0033-569X(1993)51:3<535:ESOTSA>2.0.ZU;2-S
Abstract
In this paper it is proved that the semigroup associated with the one- dimensional thermoelastic system with Dirichlet boundary conditions is an exponentially stable C0-semigroup of contraction on the space H0(1 ) x L2 x L2. The technique of the proof is completely different from t he usual energy method. It is shown that the exponential decay in D(A) recently obtained by Revira is a consequence of our main result. An i mportant application of our main result to the Linear-Quadratic-Gaussi an optimal control problem is also discussed.