Overview
- A comprehensive study of homogenized problems, focusing on the construction of nonstandard models
- Details a method for modeling processes in microinhomogeneous media (radiophysics, filtration theory, rheology, elasticity theory, and other domains)
- Complete proofs of all main results, numerous examples
- Classroom text or comprehensive reference for graduate students, applied mathematicians, physicists, and engineers
Part of the book series: Progress in Mathematical Physics (PMP, volume 46)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models.
The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: non-local models, multicomponent models, and models with memory.
Along with complete proofs of all main results, numerous examples of typical structures of microinhomogeneous media with their corresponding homogenized models are provided. Graduate students, applied mathematicians, physicists, and engineers will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text.
Reviews
From the reviews:
"The aim of homogenization theory is to establish the macroscopic behaviour of a microinhomogenous system, in order to describe some characteristics of the given heterogeneous medium. … The book is an excellent, practice oriented, and well written introduction to homogenization theory bringing the reader to the frontier of current research in the area. It is highly recommended to graduate students in applied mathematics as well as to researchers interested in mathematical modeling and asymptotical analysis." (J. Kolumban, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007)
Authors and Affiliations
Bibliographic Information
Book Title: Homogenization of Partial Differential Equations
Authors: Vladimir A. Marchenko, Evgueni Ya. Khruslov
Series Title: Progress in Mathematical Physics
DOI: https://doi.org/10.1007/978-0-8176-4468-0
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2006
Hardcover ISBN: 978-0-8176-4351-5Published: 29 November 2005
eBook ISBN: 978-0-8176-4468-0Published: 22 December 2008
Series ISSN: 1544-9998
Series E-ISSN: 2197-1846
Edition Number: 1
Number of Pages: XIV, 402
Number of Illustrations: 28 b/w illustrations
Additional Information: Translated from the original Ukrainian/Russian, "V.A.Marchenko and E.Ya.Khruslov. Homogenized models of microinhomogeneous media. Kiev, Naukova Dumka 2005."
Topics: Partial Differential Equations, Mathematical Methods in Physics, Applications of Mathematics, Complex Systems, Functional Analysis, Optimization