Homogenization: methods and applications
by Chechkin, G. A., (Gregori A.)
"The book focuses on various aspects of homogenization theory and related topics. It comprises classical results and methods of homogenization theory, as well as modern subjects and techniques developed in the last decade. Special attention is paid to averaging of random parabolic equations with lower order terms, to homogenization of singular structures and measures, and to problems with rapidly alternating boundary conditions." "The book contains many exercises, which help the reader to bette…
Read More ↓Title Statements
- Full title :Homogenization : methods and applications / G.A. Chechkin, A.L. Piatnitski, A.S. Shamaev ; translated by Tamara Rozhkovskaya.
Summary
"The book focuses on various aspects of homogenization theory and related topics. It comprises classical results and methods of homogenization theory, as well as modern subjects and techniques developed in the last decade. Special attention is paid to averaging of random parabolic equations with lower order terms, to homogenization of singular structures and measures, and to problems with rapidly alternating boundary conditions." "The book contains many exercises, which help the reader to better understand the material presented. All the main results are illustrated with a large number of examples, ranging from very simple to rather advanced."--book jacket.
Read More ↓Edition Statements
- Publication Date:©2007.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©2007.
The Physical Object
- Description:x, 234 pages : : illustrations ; : 27 cm.
Edition Identifiers
- ISBN:9780821838730, 0821838733
- oclc:ocm84838949
- LC Classification:QA377
- Dewey Decimal:515/.35
Table of Contents
Ch. 1. Related topics -- 1. Some facts of functional analysis -- 2. Some facts of ergodic theory and stochastic analysis -- 3. Elasticity system -- 4. Stokes equations -- Ch. 2. Homogenization methods -- 5. Compensated compactness -- 6. Homogenization of equations with random coefficients -- 7. Two-scale asymptotic expansion method -- 8. p-Connectedness technique (in the sense of V. V. Zhikov) -- 9. Two-scale convergence method -- 10. Homogenization of thin structures and singular measures -- 11. Method of matching asymptotic expansions -- 12. The Bogolyubov method -- Ch. 3. Applications of homogenization methods -- 13. Homogenized equations with periodic coefficients : composite materials -- 14. Filtration of viscous incompressible fluid through a porous medium : the Darcy law -- 15. Boundary value problems with rapidly alternating type of boundary conditions -- 16. Appearance of a potential (or etrange term) in the homogenized equation -- 17. Parabolic equations in media with rapidly pulsating perforation -- 18. Homogenization of nonautonomous parabolic equations with random coefficients.
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