On Reiterated Homogenization Identities
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We study homogenization of linear equations with coefficients oscillating relative to different groups of variables with periods of different smallness order. In this case, the constant effective coefficient matrix is found by successive application of classical homogenization. We construct a two-scale matrix whose effective matrix depends on the order of reiterated homogenizations. Such a dependence is not observed in some simplest cases, for example, if the spatial variable is one-dimensional or the medium has layer structure. Bibliography: 2 titles.
KeywordsDiagonal Entry Smallness Order Homogenization Procedure Homogenize Matrix Moscow State Institute
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- 2.V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals [in Russian], Nauka, Moscow (1993); English transl.: Springer, Berlin (1994).Google Scholar