Comptes Rendus
no. 10
Asymptotic behavior of the spectrum of an elliptic problem in a domain with aperiodically distributed concentrated masses
Gregory A. Chechkin1 ; Tatiana P. Chechkina2
1 Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V.Lomonosov Moscow State University, Moscow 119991, Russia
2 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow 115409, Russia
Comptes Rendus. Mécanique, Volume 345 (2017) no. 10, pp. 671-677.

In this paper, we consider a spectral problem with singular perturbation of density located near the boundary of the domain, depending on a small parameter. We prove the compactness theorem and study the behavior of eigenelements to the given problem, as the small parameter tends to zero.

Dans cet article, nous considérons un problème spectral avec une perturbation singulière de la densité située près de la limite du domaine, dépendant d'un petit paramètre. Nous prouvons le théorème de la compacité et étudions le comportement des éléments génériques du problème donné, lorsque le petit paramètre tend vers zéro.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2017.06.010
Keywords: Concentrated masses, Homogenization, Random functions
Mots-clés : Masses concentrées, Homogénéisation, Fonctions aléatoires

Gregory A. Chechkin 1; Tatiana P. Chechkina 2

1 Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V.Lomonosov Moscow State University, Moscow 119991, Russia
2 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow 115409, Russia 
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Gregory A. Chechkin; Tatiana P. Chechkina. Asymptotic behavior of the spectrum of an elliptic problem in a domain with aperiodically distributed concentrated masses. Comptes Rendus. Mécanique, Volume 345 (2017) no. 10, pp. 671-677. doi : 10.1016/j.crme.2017.06.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.06.010/

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☆ The paper was partially supported by RFBR grant 15-01-07920.

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