Exponential Stability of a Thermoelastic System with Free Boundary Conditions without Mechanical Dissipation

Authors

George Avalos, University of Nebraska-LincolnFollow
Irena Lasiecka, University of VirginiaFollow

Document Type

Article

Date of this Version

1-1-1998

Comments

Published in SIMA, Volume 29 Issue 1 pages 155–182, © 1998 Society for Industrial and Applied Mathematics. Online at http://epubs.siam.org/SIMA/volume-29/art_30082.html
Used by permission.

Abstract

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. Lagnese, Boundary Stabilization of Thin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case---where rotational forces are neglected---in [Z. Liu and S. Z. Heng, Quarterly Appl. Math., 55 (1997), pp. 551-564]). The proof is constructive in the sense that we make use of a multiplier with respect to the coupled system involved so as to generate a fortiori the desired estimates; this multiplier is of an operator theoretic nature, as opposed to the more standard differential quantities used for related work. Moreover, the particular choice of our multiplier becomes clear only after recasting the PDE model into an associated abstract evolution equation.