Nous considérons un réseau de cordes et de poutres d'Euler-Bernoulli. En utilisant une formule de Poisson généralisée et un théorème taubérien nous prouvons une formule de Weyl avec reste optimal. Comme conséquence nous prouvons des résultats d'observabilités et de stabilisations.
We consider a network of vibrating elastic strings and Euler-Bernoulli beams. 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.
@article{BSMF_2010__138_3_395_0,
author = {Ammari, Ka\"\i s and Dimassi, Mouez},
title = {Weyl formula with optimal remainder estimate of some elastic networks and applications},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
volume = {138},
year = {2010},
pages = {395-413},
doi = {10.24033/bsmf.2593},
mrnumber = {2729018},
zbl = {1205.35304},
language = {en},
url = {http://dml.mathdoc.fr/item/BSMF_2010__138_3_395_0}
}
Ammari, Kaïs; Dimassi, Mouez. Weyl formula with optimal remainder estimate of some elastic networks and applications. Bulletin de la Société Mathématique de France, Tome 138 (2010) pp. 395-413. doi : 10.24033/bsmf.2593. http://gdmltest.u-ga.fr/item/BSMF_2010__138_3_395_0/
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