Comptes Rendus
no. 8
Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tube
[Comportement asymptotique des valeurs propres du laplacien avec conditions de Neumann sur un tube extrait]

Présenté par : Évariste Sanchez-Palencia

Marina Yu. Planida1
1 The Bashkir State Pedagogical University, October Revolution st., 3a, 450000 Ufa, Russia
Comptes Rendus. Mécanique, Volume 331 (2003) no. 8, pp. 531-536.

On considère l'opérateur de Laplace dans un domaine tridimensionnel borné dont on a extrait un tube fin, avec la condition aux limites de Neumann. Nous construisons le développement asymptotique des valeurs propres pour des valeurs petites du diamètre du tube.

We consider the eigenvalue problem for the Laplace operator in a bounded three-dimensional domain where a thin tube is cut out. Imposing a Neumann boundary condition on the boundary of this tube, we construct asymptotics for eigenvalues on the small parameter that is a diameter of the tube.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(03)00125-6
Keywords: Vibrations, Asymptotique, Valeur propre
Mots-clés : Vibrations, Asymptotics, Eigenvalue

Marina Yu. Planida 1

1 The Bashkir State Pedagogical University, October Revolution st., 3a, 450000 Ufa, Russia 
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Marina Yu. Planida. Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tube. Comptes Rendus. Mécanique, Volume 331 (2003) no. 8, pp. 531-536. doi : 10.1016/S1631-0721(03)00125-6. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00125-6/

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