Asymptotic behavior of the solutions of a degenerating elliptic equation in a thin multidomain

Article type: Research Article

Authors: Prakash, Ravi | Sili, Ali^;

Affiliations: Institut Mathématique de Marseille (I2M), UMR 7373, Aix Marseille Universite, 39 rue F. Joliot Curie, 13453, Marseille cedex 13, France. E-mails: raviprakash.iisc@gmail.com, sili@univ-tln.fr

Note: [] Corresponding author. E-mail: sili@univ-tln.fr

Abstract: We study the behavior of the solutions uε of a degenerating elliptic equation in the framework of the dimension reduction problem coupled with an oscillating boundary. Under a suitable choice of the scalings on the source term and on the diffusivity coefficients, we prove that the limit problem is a nonlocal problem involving only the diffusion through the upper part of the domain.

Keywords: degenerating problem, oscillating boundary, thin domain

DOI: 10.3233/ASY-141251

Journal: Asymptotic Analysis, vol. 90, no. 3-4, pp. 345-365, 2014