| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 98 | |
| Number of page(s) | 25 | |
| DOI | https://doi.org/10.1051/cocv/2021095 | |
| Published online | 13 October 2021 | |
Riesz Basis Property and Exponential Stability for One-Dimensional Thermoelastic System with Variable Coefficients*
1
School of Mathematics and Physics, North China Electric Power University,
Beijing
102206, PR China.
2
Academy of Mathematics and Systems Science, Academia Sinica,
Beijing
100190, PR China.
** Corresponding author: bzguo@iss.ac.cn
Received:
23
April
2021
Accepted:
25
September
2021
In this paper, we study Riesz basis property and stability for a nonuniform thermoelastic system with Dirichlet-Dirichlet boundary condition, where the heat subsystem is considered as a control to the whole coupled system. By means of the matrix operator pencil method, we obtain the asymptotic expressions of the eigenpairs, which are exactly coincident to the constant coefficients case. We then show that there exists a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state space and the spectrum determined growth condition is therefore proved. As a consequence, the exponential stability of the system is concluded.
Mathematics Subject Classification: 35Q79 / 37L15 / 47B06
Key words: Thermoelastic system / variable coefficient / Riesz basis
© The authors. Published by EDP Sciences, SMAI 2021
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