Homogenization of an interface highly oscilating between two concentric ellipses

Abstract

The main purpose of the paper is to find the homogenized equation and the associate continnity conditions in the explict form of a boundary-value problem in a two-dimenatonal domain with an interface oscillating rapidly between two concentric ellipses.This boundary-value problem originates from various problema in practical applications. By the homogenization method and following the technique presented recently by Vinh and Tung [ P. C. Vinh and D. X. Tung, Mech. Res. Comm. 37 (2010), 285288; P. C. Vinh, D. X Tung, ASME J. AppL Mech., 78 (2011), 041014-1; P. C. Vinh and b. X. Tung, Acta Mech. 218 (2011), 333-348], the homogenized equation and the associate continuity conditions in the explicit form are derived.