On regular and singular perturbations of acoustic and quantum waveguides

Rustem R. Gadyl'shin

doi:10.1016/j.crme.2004.03.010

On regular and singular perturbations of acoustic and quantum waveguides

Presented by: Évariste Sanchez-Palencia

Rustem R. Gadyl'shin ^1,²

¹ Bashkir State Pedagogical University, 3a October revolution str., 450000 Ufa, Russia
² Institute of Mathematics, Ufa Science Center of Russian Academy of Sciences, 112, Chernyshevski str., 450077 Ufa, Russia

Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 647-652.

Abstract
Résumé

We consider regular and singular perturbations of the Dirichlet and Neumann boundary value problems for the Helmholtz equation in n-dimensional cylinders. The existence of eigenvalues and their asymptotics are studied.

On considère des perturbations régulières et singulières des problèmes aux limites de Dirichlet et de Neumann pour l'équation de Helmholtz dans les cylindres n-dimensionnels. Sont étudies l'existence des valeurs propres et de leur comportement asymptotique.

Received: 2004-02-20
Accepted: 2004-03-23
Published online: 2004-06-01

DOI: 10.1016/j.crme.2004.03.010

Keywords: Acoustics, Waveguide, Perturbation, Eigenvalue
Mots-clés : Acoustique, Guide d'ondes, Perturbation, Valeur propre

Author's affiliations:

Rustem R. Gadyl'shin ^{1, 2}

¹ Bashkir State Pedagogical University, 3a October revolution str., 450000 Ufa, Russia
² Institute of Mathematics, Ufa Science Center of Russian Academy of Sciences, 112, Chernyshevski str., 450077 Ufa, Russia

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Rustem R. Gadyl'shin. On regular and singular perturbations of acoustic and quantum waveguides. Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 647-652. doi : 10.1016/j.crme.2004.03.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.010/

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