An Introduction to Homogenization

Hardcover | November 11, 1999

byDoina Cioranescu, Patrizia Donato

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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 propertiesof 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 isgiven 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.

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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 propertiesof the microscopic structure. The first fou...

Doina Cioranescu (Professor, University of Paris VI and CNRS, France) Patrizia Donato (Professor, University of Rouen, France)

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Format:HardcoverPublished:November 11, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198565542

ISBN - 13:9780198565543

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Table of Contents

1. Weak and weak - convergence in Banach spaces2. Rapidly oscillating periodic functions3. Some classes of 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 caseReferences

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'serve as good textbook for a post-graduate course' ZAMM