On Homogenization of Problems in Domains of the “Infusorium” Type

Abstract

In the paper, we consider problems in perforated domains with rapidly oscillating boundary. We assume that the oscillating boundary has a special structure. The width of the “hills” has the same size as the cell of periodicity inside the domain and the order of the height of the “hills” is bigger. Under these assumptions we construct the homogenized problem, prove the homogenization theorem, construct the correctors, and obtain estimates of the deviation of the solution to the initial problem from the leading terms of the asymptotic series.