Overview
- Authors:
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V. V. Jikov
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Department of Mathematics, Pedagogical Institute of Vladimir, Vladimir, Russia
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S. M. Kozlov
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Université Aix-Provence I, Marseille, France
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O. A. Oleinik
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Department of Mathematics and Mechanics, Moscow State University, Moscow, Russia
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Table of contents (18 chapters)
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 1-54
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 55-85
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 86-132
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 133-148
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 149-186
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 187-221
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 222-249
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 250-297
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 298-322
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 323-337
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 338-366
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 367-390
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 391-414
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 415-437
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 438-459
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 460-491
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 492-501
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- V. V. Jikov, S. M. Kozlov, O. A. Oleinik
Pages 502-535
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Back Matter
Pages 536-572
About this book
It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.
Authors and Affiliations
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Department of Mathematics, Pedagogical Institute of Vladimir, Vladimir, Russia
V. V. Jikov
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Université Aix-Provence I, Marseille, France
S. M. Kozlov
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Department of Mathematics and Mechanics, Moscow State University, Moscow, Russia
O. A. Oleinik