Geodesic
Modification of unfolding approach to two-scale convergence
Mathematica Bohemica, Tome 135 (2010) no. 4, pp. 403-412

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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, 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.
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, 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.
DOI : 10.21136/MB.2010.140831
Classification : 35B27, 49J45
Keywords: homogenization; two-scale convergence; periodic unfolding 
Franců, Jan. Modification of unfolding approach to two-scale convergence. Mathematica Bohemica, Tome 135 (2010) no. 4, pp. 403-412. doi: 10.21136/MB.2010.140831
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