Comptes Rendus
no. 8
Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tube

Presented by: 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.

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.

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.

Received:
Accepted:
Published online:
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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