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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103642846610
ISBN-139783642846618
eBay Product ID (ePID)143822579
Product Key Features
Number of PagesXi, 570 Pages
LanguageEnglish
Publication NameHomogenization of Differential Operators and Integral Functionals
Publication Year2011
SubjectMechanics / General, Probability & Statistics / General, Differential Equations / Partial, Physics / Mathematical & Computational, Mathematical Analysis
TypeTextbook
Subject AreaMathematics, Science
AuthorV. V. Jikov, S. M. Kozlov, O. A. Oleinik
FormatTrade Paperback
Dimensions
Item Height0.5 in
Item Weight31 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
Number of Volumes1 vol.
IllustratedYes
Table Of Content1 Homogenization of Second Order Elliptic Operators with Periodic Coefficients.- 2 An Introduction to the Problems of Diffusion.- 3 Elementary Soft and Stiff Problems.- 4 Homogenization of Maxwell Equations.- 5 G-Convergence of Differential Operators.- 6 Estimates for the Homogenized Matrix.- 7 Homogenization of Elliptic Operators with Random Coefficients.- 8 Homogenization in Perforated Random Domains.- 9 Homogenization and Percolation.- 10 Some Asymptotic Problems for a Non-Divergent Parabolic Equation with Random Stationary Coefficients.- 11 Spectral Problems in Homogenization Theory.- 12 Homogenization in Linear Elasticity.- 13 Estimates for the Homogenized Elasticity Tensor.- 14 Elements of the Duality Theory.- 15 Homogenization of Nonlinear Variational Problems.- 16 Passing to the Limit in Nonlinear Variational Problems.- 17 Basic Properties of Abstract ?-Convergence.- 18 Limit Load.- Appendix A. Proof of the Nash-Aronson Estimate.- Appendix C. A Property of Bounded Lipschitz Domains.- References.
SynopsisThis book is an extensive study of the theory of homogenization of partial differential equations. This theory has become increasingly important in the last two decades and it forms the basis for numerous branches of physics like the mechanics of composite and perforated materials, filtration and disperse media. It will become an indispensable reference for graduate students in mathematics, physics and engineering., 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., 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.
LC Classification NumberQA299.6-433
