Volume 27, 2021
|Number of page(s)||25|
|Published online||13 October 2021|
Riesz Basis Property and Exponential Stability for One-Dimensional Thermoelastic System with Variable Coefficients*
School of Mathematics and Physics, North China Electric Power University,
102206, PR China.
2 Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, PR China.
** Corresponding author: firstname.lastname@example.org
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.