Modification of unfolding approach to two-scale convergence. (English) Zbl 1224.35020

Franců, Jan

Math. Bohem. 135, No. 4, 403-412 (2010).

Summary: Two-scale convergence is a powerful mathematical tool in periodic homogenization developed for modelling media with periodic structure. The contribution deals with the classical definition, its problems, the “dual” definition based on the so-called periodic unfolding. Since in the case of domains with boundary the unfolding operator introduced by D. Cioranescu, A. Damlamian and G.Griso does not satisfy the crucial integral preserving property, the contribution proposes a modified unfolding operator which satisfies the property and thus simplifies the theory. The properties of two-scale convergence are surveyed.

MSC:

35B27	Homogenization in context of PDEs; PDEs in media with periodic structure
49J45	Methods involving semicontinuity and convergence; relaxation

Keywords:

homogenization; two-scale convergence; periodic unfolding