
An Introduction to Homogenization
Oxford University Press
Published on 11. November 1999
Book
Hardback
272 pages
978-0-19-856554-3 (ISBN)
Description
This book provides an introduction to the mathematical theory of homogenization, which describes the replacement of a real composite material by a fictitious homogeneous one. The aim of the theory is to describe the macroscopic properties of the composite by taking into account the properties of the microscopic structure. The first four chapters cover variational methods for partial differential equations, which is the natural framework of homogenization theory. The text then discusses the homogenization of several kinds of second order boundary value problems. Particular attention is given to the classical examples of the steady and non-steady heat equations, the wave equation and the linearized system of elasticity. All topics are illustrated by figures and numerous examples.
Reviews / Votes
'serve as good textbook for a post-graduate course' ZAMMMore details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Illustrations
numerous mathematical examples
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 19 mm
Weight
578 gr
ISBN-13
978-0-19-856554-3 (9780198565543)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Doina Cioranescu (Professor, University of Paris VI and CNRS, France) Patrizia Donato (Professor, University of Rouen, France)
Author
Directeur de Recherche, Centre National de la Recherche ScientifiqueDirecteur de Recherche, Centre National de la Recherche Scientifique, University of Paris VI
Professor, Department of MathematicsProfessor, Department of Mathematics, University of Rouen
Content
1. Weak and weak - convergence in Banach spaces ; 2. Rapidly oscillating periodic functions ; 3. Some classes of Sobolev spaces ; 4. Some variational elliptic problems ; 5. Examples of periodic composite materials ; 6. Homogenization of elliptic equations: the convergence result ; 7. The multiple-scale method ; 8. Tartar's method of oscillating test functions ; 9. The two-scale convergence method ; 10. Homogenization in linearized elasticity ; 11. Homogenization of the heat equation ; 12. Homogenization of the wave equation ; 13. General Approaches to the non-periodic case ; References