Progress in Mathematical Physics

Homogenization of Partial Differential Equations

Authors: Marchenko, Vladimir A., Khruslov, Evgueni Ya.

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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)


Table of contents (8 chapters)

  • Introduction

    Pages 1-29

  • The Dirichlet Boundary Value Problem in Strongly Perforated Domains with Fine-Grained Boundary

    Pages 31-65

  • The Dirichlet Boundary Value Problem in Strongly Perforated Domains with Complex Boundary

    Pages 67-104

  • Strongly Connected Domains

    Pages 105-135

  • The Neumann Boundary Value Problems in Strongly Perforated Domains

    Pages 137-209

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-0-8176-4468-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-0-8176-4351-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Homogenization of Partial Differential Equations
Authors
Series Title
Progress in Mathematical Physics
Series Volume
46
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4468-0
DOI
10.1007/978-0-8176-4468-0
Hardcover ISBN
978-0-8176-4351-5
Series ISSN
1544-9998
Edition Number
1
Number of Pages
XIV, 402
Number of Illustrations and Tables
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."
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