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Homogenization of differential operators. (Усреднение дифференциальных операторов.) (Russian. English summary) Zbl 0801.35001
Moskva: Izdatel’skaya Firma “Fiziko-Matematicheskaya Literatura”. 464 p. (1993).
This interesting book (monograph) concerns the already well developed theory of homogenization. It provides us with the mathematical foundations of the theory, as well as it indicates various relations with other theories of mathematics, physics and mechanics like, for example, ergodic theory, the theory of composite materials, etc.
The book contains, for instance, the homogenization of differential equations of elliptic or parabolic type with periodic, almost periodic or random coefficients. There are many examples and solutions to important physical problems such as diffusion in random media, elasticity problems in perforated or stratified domains and so on.
Some of the 17 chapters of the book are devoted to such problems as \(G\)- convergence of differential operators, \(\Gamma\)-convergence of functionals, homogenization of nonlinear variational problems, spectral problems of homogenization theory, boundary value problems in perforated random domains, homogenization and percolation, etc. Many references to the current literature on the subject are also given.

MSC:
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
47F05 General theory of partial differential operators
74E05 Inhomogeneity in solid mechanics
74E30 Composite and mixture properties
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