Asymptotically sharp uniform estimates in a scalar spectral stiff problem

Miguel Lobo; Serguei A. Nazarov; Eugenia Pérez

doi:10.1016/S1631-0721(03)00073-1

Asymptotically sharp uniform estimates in a scalar spectral stiff problem
[Estimations asymptotiques uniformes pour le spectre d'un problème scalaire raide]

Présenté par : Évariste Sanchez-Palencia

Miguel Lobo ¹ ; Serguei A. Nazarov ² ; Eugenia Pérez ³

¹ Departamento de Matemáticas, Estadı́stica y Computación, Universidad de Cantabria, Av. de los Castros, s/n. 39005 Santander, Spain
² Institute of Mechanical Engineering Problems, RAN V. O. Bol'shoi pr., 61, 199178 St Petersburg, Russia
³ Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Av. de los Castros, s/n. 39005 Santander, Spain

Comptes Rendus. Mécanique, Volume 331 (2003) no. 5, pp. 325-330.

Résumé
Abstract

On obtienent des estimations de la vitesse de convergence des valeurs propres, convenablement mises a l'échelle, d'un problème de Neumann raide pour l'operateur de Laplace. Des bornes correspondantes a ces estimations sont exprimées en termes du rapport des raideurs et des propriétés du spectre limite dans les rangs des fréquences basses et moyennes.

Estimates of convergence rates for rescaled eigenvalues of the stiff Neumann problem for the Laplacian are obtained. The bounds are expressed in terms of the stiffness ratio and properties of the limit spectrum both for low and middle frequency ranges.

Reçu le : 2003-02-14
Accepté le : 2003-03-18
Publié le : 2003-04-26

DOI : 10.1016/S1631-0721(03)00073-1

Keywords: Acoustics, Waves, Vibrations, Stiff problem, Spectral analysis, Low frequencies, Middle frequencies
Mots-clés : Acoustique, Ondes, Vibrations, Problème raide, Analyse spectrale, Basses fréquences, Moyennes fréquences

Affiliations des auteurs :

Miguel Lobo ¹ ; Serguei A. Nazarov ² ; Eugenia Pérez ³

¹ Departamento de Matemáticas, Estadı́stica y Computación, Universidad de Cantabria, Av. de los Castros, s/n. 39005 Santander, Spain
² Institute of Mechanical Engineering Problems, RAN V. O. Bol'shoi pr., 61, 199178 St Petersburg, Russia
³ Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Av. de los Castros, s/n. 39005 Santander, Spain

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     title = {Asymptotically sharp uniform estimates in a scalar spectral stiff problem},
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Miguel Lobo; Serguei A. Nazarov; Eugenia Pérez. Asymptotically sharp uniform estimates in a scalar spectral stiff problem. Comptes Rendus. Mécanique, Volume 331 (2003) no. 5, pp. 325-330. doi : 10.1016/S1631-0721(03)00073-1. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00073-1/

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V. Chiadò Piat; L. D’Elia; S.A. Nazarov The stiff Neumann problem: Asymptotic specialty and “kissing” domains, Asymptotic Analysis, Volume 128 (2022) no. 1, p. 113 | DOI:10.3233/asy-211701
Delfina Gómez; Sergey A. Nazarov; Maria–Eugenia Pérez-Martínez A Dirichlet Spectral Problem in Domains Surrounded by Thin Stiff and Heavy Bands, Computational and Analytic Methods in Science and Engineering (2020), p. 101 | DOI:10.1007/978-3-030-48186-5_6
Delfina Gómez; Santiago Navazo-Esteban; María-Eugenia Pérez-Martínez A Stiff Problem: Stationary Waves and Approximations, Integral Methods in Science and Engineering (2019), p. 133 | DOI:10.1007/978-3-030-16077-7_11
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