An Introduction to Homogenization

by Doina Cioranescu, Patrizia Donato

Overview

Composite materials are widely used in industry and include such well known examples as superconductors and optical fibers. However, modeling these materials is difficult, since they often has different properties at different points. The mathematical theory of homogenization is designed to handle this problem. The theory uses an idealized homogenous material to model a real composite while taking into account the microscopic structure. This introduction to homogenization theory develops the natural framework of the theory with four chapters on variational methods for partial differential equations. It then discusses the homogenization of several kinds of second-order boundary value problems. It devotes separate chapters to the classical examples of stead and non-steady heat equations, the wave equation, and the linearized system of elasticity. It includes numerous illustrations and examples.

Product Details

ISBN-13:	9780198565543
Publisher:	Oxford University Press
Publication date:	02/24/2000
Series:	Oxford Lecture Series in Mathematics and Its Applications , #17
Edition description:	New Edition
Pages:	272
Product dimensions:	9.21(w) x 6.14(h) x 0.63(d)

About the Author

University of Paris

University of Rouen

Table of Contents

Introduction1. Weak and weak]*-convergences in Banach spaces2. Rapidly oscillating periodic functions3. Some classes in Sobolev spaces4. Some variational elliptic problems5. Examples of periodic composite materials6. Homogenization of elliptic equations: the convergence result7. The multiple-scale method8. Tartar's method of oscillating test functions9. The two-scale convergence method10. Homogenization in linearized elasticity11. Homogenization of the heat equation12. Homogenization of the wave equation13. General approaches to the non-periodic caseBibliographyIndex