Homogénéisation du problème de Neumann non homogène dans des ouverts perfores

Article type: Research Article

Authors: Cioranescu, Doina^; | Donato, Patrizia

Affiliations: Laboratoire d'Analyse Numérique (U.A. 189), Université Pierre et Marie Curie (Paris VI), 75252 Paris Cedex 05, France

Note: [] Adresse permanente: Dipartimento di Maternatica e Applicazioni, Università di Napoli, 80134 Napoli, l'Italie. Ce travail a été effectué lors d'un séjour au Laboratoire d'Analyse Numérique de l'Université Pierre et Marie Curie (Paris VI) au cours de l'année universitaire 86–87 en qualité de boursière du C.N.R. (Consiglio Nazionale delle Ricerche).

Abstract: We consider the Neumann problem in a domain with periodic holes. The size of the basic cell and of the holes is of order of ε. Some homogenization theorems are proved. There are essentially two limit cases as ε→0. In the first one the mean value of the data on the boundary of the holes is nonzero. This term gives rise to a nonzero contribution in the right-hand side of the homogenized equation. In the second case, when this mean value is zero, the same homogenized equation as for the homogeneous Neumann problem is obtained. General Fourier conditions are also treated.

DOI: 10.3233/ASY-1988-1203

Journal: Asymptotic Analysis, vol. 1, no. 2, pp. 115-138, 1988