WORST SCENARIO METHOD IN HOMOGENIZATION. LINEAR CASE

摘要

The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlavacek (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized gradient in the places where these components change and on the average of homogenized solution in some critical subdomain.