Comptes Rendus
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]
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
Mot clés : Vibrations, Asymptotics, Eigenvalue

Marina Yu. Planida 1

1 The Bashkir State Pedagogical University, October Revolution st., 3a, 450000 Ufa, Russia
@article{CRMECA_2003__331_8_531_0,
     author = {Marina Yu. Planida},
     title = {Asymptotics for eigenvalues of the {Laplacian} with a {Neumann} boundary condition on a thin cut-out tube},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {531--536},
     publisher = {Elsevier},
     volume = {331},
     number = {8},
     year = {2003},
     doi = {10.1016/S1631-0721(03)00125-6},
     language = {en},
}
TY  - JOUR
AU  - Marina Yu. Planida
TI  - Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tube
JO  - Comptes Rendus. Mécanique
PY  - 2003
SP  - 531
EP  - 536
VL  - 331
IS  - 8
PB  - Elsevier
DO  - 10.1016/S1631-0721(03)00125-6
LA  - en
ID  - CRMECA_2003__331_8_531_0
ER  - 
%0 Journal Article
%A Marina Yu. Planida
%T Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tube
%J Comptes Rendus. Mécanique
%D 2003
%P 531-536
%V 331
%N 8
%I Elsevier
%R 10.1016/S1631-0721(03)00125-6
%G en
%F CRMECA_2003__331_8_531_0
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/

[1] M.Yu. Planida On the convergence of solutions of singularly perturbed boundary-value problems for the Laplace operator, Math. Notes, Volume 71 (2002), pp. 867-877

[2] A.M. Il'in Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, American Mathematical Society, Providence, RI, 1992

[3] R.R. Gadyl'shin Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition, Math. Notes, Volume 52 (1992), pp. 1020-1029

[4] M.Yu. Planida Asymptotics of eigenvalues for a cylinder insulated on a narrow strip, Comput. Math. Math. Phys., Volume 43 (2003), pp. 403-413

[5] S.A. Nazarov, M.V. Paukshto, Discrete models and homogenization in problems of elastisity theory, Lenigrad University, Leningrad, 1984 (in Russian)

[6] S. Ozawa Spectra of domains spherical Neumann boundary, J. Fac. Sci. Univ. Tokyo Sect. IA Math., Volume 30 (1983), pp. 259-277

[7] V.G. Maz'ya; S.A. Nazarov; B.A. Plamenevskij Asymptotic expansions of the eigenvalues of boundary value problems for the Laplace operator in domains with small holes, Math. USSR-Izv., Volume 24 (1985), pp. 321-345

Cité par Sources :

Commentaires - Politique