Overview
Homogenization is a method for modelling processes in complex structures. These processes are far too complex for analytic and numerical methods and are best described by PDEs with rapidly oscillating coefficients - a technique that has become increasingly important in the last three decades due to its multiple applications in the areas of optimization, radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. The present monograph is a comprehensive study of homogenization problems describing various physical processes in micro-inhomogeneous media. From the technical viewpoint the work focuses on the construction of nonstandard models for media characterized by several small-scale parameters (multiscale models). A variety of techniques are used --- specifically functional analysis, the spectral theory for differential operators, the Laplace transform, and, most importantly, a new variational PDE method for studying the asymptotic behavior of solutions of stationary boundary value problems. This new method can be applied to a wide variety of problems.Key topics in this systematic exposition include asymptotic analysis, Dirichlet- and Neumann-type boundary value problems, differential equations with rapidly oscillating coefficients, homogenization, homogenized and non-local models. Along with complete proofs of all main results, numerous examples of typical structures of micro-inhomogeneous media with their corresponding homogenized models are provided. Applied mathematicians, advanced-level graduate students, physicists, engineers, and specialists in mechanics will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text.
Full Product Details
Author: Vladimir A. Marchenko ,
Evgueni Ya. Khruslov
Publisher: Birkhauser Boston Inc
Imprint: Birkhauser Boston Inc
Edition: 2006 ed.
Volume: 46
Dimensions:
Width: 15.50cm
, Height: 2.30cm
, Length: 23.50cm
Weight: 1.680kg
ISBN: 9780817643515
ISBN 10: 0817643516
Pages: 402
Publication Date: 29 November 2005
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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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)
From the reviews: <p> 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. a ] 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)
