The Neumann problem in thin domains with very highly oscillatory boundaries

Author(s)

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

Affiliation

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

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

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 404, n. 1, p. 86-104, AUG 1 2013.
• Web of Science Citations: 20

Abstract

In this paper, we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type R-is an element of = [(x(1), x(2)) is an element of R-2 vertical bar x(1) is an element of (0, 1), -is an element of b(X-1) < x(2) < is an element of G(x(1), X-1/is an element of(alpha))] with alpha > 1 and is an element of > 0, defined by smooth functions b(x) and G(x, y), where the function G is supposed to be l(x) -periodic in the second variable y. The condition alpha > 1 implies that the upper boundary of this thin domain presents a very high oscillatory behavior. Indeed, we have that the order of its oscillations is larger than the order of the amplitude and height of R-is an element of given by the small parameter c. We also consider more general and complicated geometries for thin domains which are not given as the graph of certain smooth functions, but rather more comb-like domains. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 11/08929-3 - Asymptotic and geometric behavior of partial differential equations
• Grantee: Marcone Corrêa Pereira
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 10/18790-0 - Asymptotic behavior and geometric of partial differential equations
• Grantee: Marcone Corrêa Pereira
• Support Opportunities: Regular Research Grants