Weyl formula with optimal remainder estimate of some elastic networks and applications
Bulletin de la Société Mathématique de France, Volume 138 (2010) no. 3, p. 395-413

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.

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.

DOI : https://doi.org/10.24033/bsmf.2593
Classification:  35P20,  93D15,  93D20
Keywords: networks of strings, networks of Euler-Bernoulli beams, tauberian theorem, Weyl formula
@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {138},
     number = {3},
     year = {2010},
     pages = {395-413},
     doi = {10.24033/bsmf.2593},
     zbl = {1205.35304},
     mrnumber = {2729018},
     language = {en},
     url = {http://www.numdam.org/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, Volume 138 (2010) no. 3, pp. 395-413. doi : 10.24033/bsmf.2593. http://www.numdam.org/item/BSMF_2010__138_3_395_0/

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