Homogenization in a thin domain with an oscillatory boundary

Author(s)

Arrieta, Jose M. ^[1] ; Pereira, Marcone C. ^[2]

Affiliation

^[1] Univ Complutense Madrid, Dept Matemat Aplicada, Fac Matemat, E-28040 Madrid - Spain

^[2] Univ Sao Paulo, Escola Artes Ciencias & Humanidades, Sao Paulo - Brazil

• Document type: Journal article
• Source: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 96, n. 1, p. 29-57, JUL 2011.
• Web of Science Citations: 31

Abstract

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type R(epsilon) = [(x(1), x(2)) is an element of R(2) vertical bar x(1) is an element of (0, 1), 0 < x(2) < epsilon G(x(1), x(1)/epsilon)] where the function G(x, y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter epsilon. (C) 2011 Elsevier Masson SAS. All rights reserved. (AU)