Volume 26, 2020
|Number of page(s)||16|
|Published online||19 February 2020|
Laboratoire M2N, EA7340, CNAM,
292 rue Saint-Martin,
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: email@example.com
Accepted: 27 November 2019
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.
© The authors. Published by EDP Sciences, SMAI 2020
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