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© 2006

Homogenization of Partial Differential Equations

Benefits

  • 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

Book

Part of the Progress in Mathematical Physics book series (PMP, volume 46)

About this book

Introduction

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.

Keywords

Boundary value problem asymptotic analysis complexity differential equation elasticity mechanics modeling partial differential equation standard model

Authors and affiliations

  1. 1.Physics and Engineering Mathematical DivisionB. Verkin Institute for Low TemperatureKharkovUkraine

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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)