Homogenization of parabolic equations with contrasting coefficients
Gennadiy V. Sandrakov · Izvestiya Mathematics · 1999
We consider non-stationary diusion problems in a periodic medium with inclusions lled with a material of small conductivity. We propose homoge- nized equations whose solutions approximate those of the problems under consider- ation. We prove estimates for the accuracy of this approximation as the period of the medium and the conductivity coecient tend to zero. The form of the homog- enized equations and the accuracy estimates depend essentially on the asymptotic behaviour of the conductivity coecient in relation to the square of the period. x 1. Introduction In this paper we consider non-stationary parabolic equations whose coecients depend on two small positive parameters and The small-scale parameter determines the period of the coecients of these equations, and the contrast param- eter characterizes the ratio of the minimal and maximal values of the conductivity coecients. Initial-boundary value problems for these equations simulate diusion in a medium with inclusions of small conductivity that are located periodically with period . We assume that, as 0, we have ! 0 and one of the following three conditions: