[Comportement asymptotique à l'infini d'un problème de Neumann dans une couche perforée]
On considère un problème de Neumann dans un domaine , 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 , 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.
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Mot clés : Mécanique des solides numérique, Couche périodique, Processus d'homogénéisation, Comportement asymptotique, Espaces avec poids
@article{CRMECA_2003__331_1_85_0,
author = {Sergue{\i}\ensuremath{\ddot{}} A. Nazarov and Gudrun Th\"ater},
title = {Asymptotics at infinity of solutions to the {Neumann} problem in a sieve-type layer},
journal = {Comptes Rendus. M\'ecanique},
pages = {85--90},
publisher = {Elsevier},
volume = {331},
number = {1},
year = {2003},
doi = {10.1016/S1631-0721(02)00005-0},
language = {en},
}
TY - JOUR AU - Sergueı̈ A. Nazarov AU - Gudrun Thäter TI - Asymptotics at infinity of solutions to the Neumann problem in a sieve-type layer JO - Comptes Rendus. Mécanique PY - 2003 SP - 85 EP - 90 VL - 331 IS - 1 PB - Elsevier DO - 10.1016/S1631-0721(02)00005-0 LA - en ID - CRMECA_2003__331_1_85_0 ER -
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/
[1] Plates and Junctions in Elastic Multi-Structures. An Asymptotic Analysis, Masson, Paris, 1990
[2] Approximation of a two dimensional problem of junctions, Comput. Mech., Volume 6 (1990), pp. 435-455
[3] Asymptotics of the spectrum of the Neumann problem in singularly perturbed thin domains, Leningr. Math. J., Volume 2 (1991), pp. 287-311
[4] Asymptotic analysis of a mixed boundary value problem in a multi-structure, Asymptotic Anal., Volume 8 (1994), pp. 105-143
[5] Junctions of singularly degenerating domains with different limit dimensions. 1 & 2, Trudy Sem. Petrovsk., Volume 18 (1995), pp. 3-78 and 20 (1997) 155–195
[6] Asymptotics of the solution to a boundary value problem in a thin cylinder with nonsmooth lateral surface, Math. Izvestiya, Volume 42 (1994), pp. 183-217
[7] Asymptotic expansions at infinity of solutions to the elasticity theory problem in a layer, Trudy Moskov. Mat. Obschch., Volume 60 (1998), pp. 3-97
[8] The asymptotic properties of the solution to the Stokes problem in domains that are layer-like at infinity, J. Math. Fluid Mech., Volume 1 (1999), pp. 131-167
[9] Asymptotics at infinity of the solution to the Dirichlet problem for a system of equations with periodic coefficients in an angular domain, Russian J. Math. Phys., Volume 3 (1995), pp. 297-326
[10] Non-Homogeneous Media and Vibration Theory, Lecture Notes in Phys., 127, Springer-Verlag, Berlin, 1980
[11] Homogenisation: Averaging Processes in Periodic Media. Mathematical Problems in the Mechanics of Composite Materials, Kluwer Academic, Dordrecht, 1989
[12] Vishik–Lyusternik method for elliptic boundary-value problems in regions with conical points. 1. The problem in a cone, Siberian Math. J., Volume 22 (1982), pp. 594-611
[13] Boundary problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc., Volume 16 (1967), pp. 227-313
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