Comptes Rendus
no. 1-2
Partial Differential Equations
Observation of some elastic networks

Presented by: Jean-Michel Bony

Kaïs Ammari1 ; Mouez Dimassi2
1 Département de mathématiques, faculté des sciences, Université de Monastir, 5019 Monastir, Tunisie
2 Département de mathématiques, Institut Galilée, Université Paris 13, 99, avenue Jean-Baptiste-Clément, 93430 Villetaneuse, France
Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 33-37.

We consider a network of vibrating elastic strings. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results.

Nous considérons un réseau de cordes. En utilisant une formule de Poisson généralisée et un théorème Taubérien nous prouvons une formule de Weyl avec reste optimal. Comme conséquence nous prouvons un résultat d'observablité et de stabilisation.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.11.008

Kaïs Ammari 1; Mouez Dimassi 2

1 Département de mathématiques, faculté des sciences, Université de Monastir, 5019 Monastir, Tunisie
2 Département de mathématiques, Institut Galilée, Université Paris 13, 99, avenue Jean-Baptiste-Clément, 93430 Villetaneuse, France 
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Kaïs Ammari; Mouez Dimassi. Observation of some elastic networks. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 33-37. doi : 10.1016/j.crma.2008.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.008/

[1] K. Ammari, M. Dimassi, Weyl formula with optimal remainder estimate of some elastic networks and applications, submitted for publication

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