Homogenization of Differential Operators and Integral Functionals
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Product details:
- Edition number Softcover reprint of the original 1st ed. 1994
- Publisher Springer Berlin Heidelberg
- Date of Publication 16 December 2011
- Number of Volumes 1 pieces, Book
- ISBN 9783642846618
- Binding Paperback
- See also 9783540548096
- No. of pages570 pages
- Size 235x155 mm
- Weight 879 g
- Language English
- Illustrations XI, 570 p. 0
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Long description:
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. This 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.
MoreTable of Contents:
1 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.
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