[Domaines minces localement périodiques avec une période variable]
Nous analysons le comportement des solutions de l'équation de Laplace dans un domaine mince à frontière fortement oscillante. Les oscillations sont localement périodiques dans le sens où l'amplitude et la période ne sont pas nécessairement constantes, puisqu'elles varient en espace. Nous obtenons le problème limite homogénéisé et montrons les résultats des correcteurs. Pour atteindre notre objectif, nous étendons la méthode de l'opérateur d'éclatement à des cas localement périodiques. Les idées principales de cette extension peuvent être appliquées à d'autres cas, comme par exemple à des domaines perforés ou à des structures réticulées localement périodiques dont la période n'est pas forcément constante.
We analyze the behavior of the solutions of the Laplace equation with Neumann boundary conditions in a thin domain with a highly oscillatory behavior. The oscillations are locally periodic in the sense that both the amplitude and the period of the oscillations may not be constant and actually they vary in space. We obtain the asymptotic homogenized limit and provide some correctors. To accomplish this goal, we extend the unfolding operator method to the locally periodic case. The main ideas of this extension may be applied to other cases like perforated domains or reticulated structures, which are locally periodic with not necessarily a constant period.
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@article{CRMATH_2014__352_5_397_0,
author = {Arrieta, Jos\'e M. and Villanueva-Pesqueira, Manuel},
title = {Locally periodic thin domains with varying period},
journal = {Comptes Rendus. Math\'ematique},
pages = {397--403},
publisher = {Elsevier},
volume = {352},
number = {5},
year = {2014},
doi = {10.1016/j.crma.2014.03.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.03.014/}
}
TY - JOUR AU - Arrieta, José M. AU - Villanueva-Pesqueira, Manuel TI - Locally periodic thin domains with varying period JO - Comptes Rendus. Mathématique PY - 2014 SP - 397 EP - 403 VL - 352 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.03.014/ DO - 10.1016/j.crma.2014.03.014 LA - en ID - CRMATH_2014__352_5_397_0 ER -
%0 Journal Article %A Arrieta, José M. %A Villanueva-Pesqueira, Manuel %T Locally periodic thin domains with varying period %J Comptes Rendus. Mathématique %D 2014 %P 397-403 %V 352 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.03.014/ %R 10.1016/j.crma.2014.03.014 %G en %F CRMATH_2014__352_5_397_0
Arrieta, José M.; Villanueva-Pesqueira, Manuel. Locally periodic thin domains with varying period. Comptes Rendus. Mathématique, Tome 352 (2014) no. 5, pp. 397-403. doi : 10.1016/j.crma.2014.03.014. http://www.numdam.org/articles/10.1016/j.crma.2014.03.014/
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