Journal of Mathematical Sciences

, Volume 205, Issue 2, pp 297–303 | Cite as

On Reiterated Homogenization Identities

  • S. E. Pastukhova
  • R. N. Tikhomirov

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.


Diagonal Entry Smallness Order Homogenization Procedure Homogenize Matrix Moscow State Institute 
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  1. 1.
    S. E. Pastukhova and R. N. Tikhomirov, “Operator estimates in reiterated and locally periodic homogenization” [in Russian], Dokl. Akad. Nauk, Ross. Akad. Nauk 415, No. 3, 304–309 (2007); English transl.: Dokl. Math. 76, No. 1, 548–553 (2007).CrossRefMATHMathSciNetGoogle Scholar
  2. 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

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Moscow State Institute of Radio EngineeringElectronics and Automation (Technical University)MoscowRussia
  2. 2.Vladimir State UniversityVladimirRussia

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