Comptes Rendus
no. 1
Asymptotics at infinity of solutions to the Neumann problem in a sieve-type layer
[Comportement asymptotique à l'infini d'un problème de Neumann dans une couche perforée]

Présenté par : Évariste Sanchez-Palencia

Sergueı̈ A. Nazarov1 ; Gudrun Thäter2
1 Inst. of Mechanical Engineering Problems, V. O. Bol'shoı̈ pr. 61, St. Petersburg, 199178, Russia
2 Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 85-90.

On considère un problème de Neumann dans un domaine Ω, qui coincide avec une couche périodique excepté sur une partie compacte. On démontre que l'opérateur correspondant satisfait à la propriété de Fredholm dans des espaces de Sobolev avec poids et on détermine son noyau et son conoyau. Tous ces résultats sont déduits de la représentation asymptotique des solutions à l'infini.

The Neumann problem is considered in a domain Ω, which can differ from a periodic layer inside a compact set. We prove the Fredholm property of the corresponding operator in step-weighted Sobolev spaces and determine its kernel and cokernel. All these results are based on the obtained asymptotic representation of solutions at infinity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(02)00005-0
Keywords: Computational solid mechanics, Periodic layer, Homogenization procedure, Asymptotic behaviour, Step-weighted spaces
Mots-clés : Mécanique des solides numérique, Couche périodique, Processus d'homogénéisation, Comportement asymptotique, Espaces avec poids

Sergueı̈ A. Nazarov 1 ; Gudrun Thäter 2

1 Inst. of Mechanical Engineering Problems, V. O. Bol'shoı̈ pr. 61, St. Petersburg, 199178, Russia
2 Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany 
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Sergueı̈ A. Nazarov; Gudrun Thäter. Asymptotics at infinity of solutions to the Neumann problem in a sieve-type layer. Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 85-90. doi : 10.1016/S1631-0721(02)00005-0. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)00005-0/

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