Homogenized Models of Composite Media

  • E. Ya. Khruslov
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 5)


In this paper we consider some homogenized models, which arise in consequence homogenization of boundary-value problems describing physical processes in highly inhomogeneous media. Such media take place, for example, in theory filtration, applied superconductivity,etc. Physical processes in them are described by both boundary-value problems in highly perforated domains and partial differential equations with rapidly oscillating coefficients, which do not satisfy conditions of uniform ellipticity or boundedness. The homogenization of such problems leads to unusual homogenized models (nonlocal, multiphase models, model with memory and others).


Homogenize Equation Neumann Problem Homogenize Model Homogenize Problem Composite Medium 
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  1. [1]
    V.A.Marchenko and E.Ya.Khruslov, “Boundary-value problems in domains with fine-grained boundaries”, Naukova Dumka, Kiev, 1974, 278p.Google Scholar
  2. [2]
    E.Ya.Khruslov, “The asymptotic behaviour of the solution of the second boundary-value problem for diminution of grains of the boundary”, Mat, Sbomik 106 No 4 (1978)Google Scholar
  3. [3]
    E.Ya.Khruslov, “On convergence of the solution of the second boundary-value problem in weakly connected domains”, In: “Theory of operators in functional spaces and its applications” (in Rus.), Naukova Dumka, Kiev, 1981.Google Scholar
  4. [4]
    E.Ya.Khruslov, “Homogenized models of diffusion in cracked-porous media”, Dokl. AN SSSR, 309 No 2, 1989Google Scholar
  5. [5]
    G.I. Barenblat, V.M.Entov and V.M.Ryzhik, “Motion of liquids and gases in natural layers” (in Rus.), Nauka, Moscow, (1984),208p.Google Scholar
  6. [6]
    V.N.Fenchenko and E.Ya.Khruslov, “Asymptotic of of solution of differential equations the with strongly oscillating matrix of coefficients which which does not satisfy the condition of uniform boundedness”, Dokl. AN Ukr.SSR, No. 4,(1981).Google Scholar
  7. [7]
    V.N.Fenchenko and E.Ya.Khruslov, “Asymptotic of solution of differential equations with strongly oscillating and degenerating matrix of coefficients”, Dokl. AN Ukr.SSR, No.4,(1980).Google Scholar
  8. [8]
    E.Ya.Khruslov, “A homogenized model of highly inhomogeneous medium with memory”, Uspekhi Matem. Nauk. (1990)Google Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • E. Ya. Khruslov
    • 1
  1. 1.Physico-Technical Institute of Low TemperaturesUkrainian SSR Academy of SciencesKharkovUSSR

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