The periodic unfolding method for perforated domains and Neumann sieve models
نویسندگان
چکیده
The periodic unfolding method, introduced in [D. Cioranescu, A. Damlamian, G. Griso, Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104], was developed to study the limit behavior of periodic problems depending on a small parameter ε. The same philosophy applies to a range of periodic problems with small parameters and with a specific period (as well as to almost any combinations thereof). One example is the so-called Neumann sieve. In this work, we present these extensions and show how they apply to known results and allow for generalizations (some in dimension N 3 only). The case of the Neumann sieve is treated in details. This approach is significantly simpler than the original ones, both in spirit and in practice. © 2007 Elsevier Masson SAS. All rights reserved. Résumé La méthode de l’éclatement périodique, introduite dans [D. Cioranescu, A. Damlamian, G. Griso, Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104], a pour but l’étude du comportement asymptotique de problèmes périodiques avec période tendant vers zéro. La même approche permet de traiter toute une famille de problèmes caractérisés par des périodicités de tailles tendant vers zéro. Un exemple est donné par le problème connu sous le nom de la passoire de Neumann. Nous présentons ici divers prolongements et généralisations de l’éclatement périodique (certains nécéssitant que la dimension N soit supérieure à 3) et nous l’appliquons à la passoire de Neumann. Pour ce type de problèmes, cette approche apparaît comme élémentaire, directe et plus efficace que les méthodes classiques. © 2007 Elsevier Masson SAS. All rights reserved.
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