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This article is cited in 261 scientific papers (total in 261 papers)
On an extension of the method of two-scale convergence and its applications
V. V. Zhikov Vladimir State Pedagogical University
Abstract:
The concept of two-scale convergence associated with a fixed periodic Borel measure $\mu$ is introduced. In the case when $d\mu=dx$ is Lebesgue measure on the torus convergence in the sense of Nguetseng–Allaire is obtained. The main properties of two-scale convergence are revealed by the simultaneous consideration of a sequence of functions and a sequence of their gradients. An application of two-scale convergence to the homogenization of some problems in the theory of porous media (the double-porosity model) is presented. A mathematical notion of “softly or weakly coupled parallel flows” is worked out. A homogenized operator is constructed and the convergence result itself is interpreted as a “strong two-scale resolvent convergence”. Problems concerning the behaviour of the spectrum under homogenization are touched upon in this connection.
Received: 19.04.1999 and 17.02.2000
Citation:
V. V. Zhikov, “On an extension of the method of two-scale convergence and its applications”, Mat. Sb., 191:7 (2000), 31–72; Sb. Math., 191:7 (2000), 973–1014
Linking options:
https://www.mathnet.ru/eng/sm491https://doi.org/10.1070/sm2000v191n07ABEH000491 https://www.mathnet.ru/eng/sm/v191/i7/p31
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Abstract page: | 1661 | Russian version PDF: | 497 | English version PDF: | 41 | References: | 110 | First page: | 1 |
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