| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 19 | |
| Number of page(s) | 16 | |
| DOI | https://doi.org/10.1051/cocv/2019075 | |
| Published online | 19 February 2020 | |
An extension of a Lyapunov approach to the stabilization of second order coupled systems*,**,***
1
Laboratoire M2N, EA7340, CNAM,
292 rue Saint-Martin,
75003
Paris France.
2
Université de Carthage, Institut Préparatoire aux Etudes Scientifiques et Techniques,
B.P. 51 2070
La Marsa, Tunisia.
3
Laboratoire équations aux dérivées partielles, Faculté des sicences de Tunis, Université Tunis El Manar, Campus Universitaire El Manar,
2092
El Manar, Tunisia.
**** Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
27
March
2019
Accepted:
27
November
2019
Abstract
This paper deals with the convergence to zero of the energy of the solutions of a second order linear coupled system. It revisits some previous results on the stabilization of such systems by exhibiting Lyapunov functions. The ones used are constructed according to some scalar cases situations. These simpler situations explicitely show that the assumptions made on the operators in the coupled systems seem, first, natural and, second, give insight on their forms.
Mathematics Subject Classification: 35B40 / 49J15 / 49J20
Key words: damping / linear evolution equations / dissipative hyperbolic equation / decay rates / Lyapunov function
The first author wishes to thank the Tunisian Mathematical Society (SMT) for its kind invitation to its annual congress during which this work was completed.
The second author wishes to thank the department of mathematics and statistics EPN6 and the research department M2N (EA7340) of the CNAM where this work was initiated.
Both authors are grateful to the reviewers for their helpful comments and suggestions.
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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