Introduction to Homogenization

Zusatztext 'serve as good textbook for a post-graduate course' ZAMM Informationen zum Autor Doina Cioranescu (Professor, University of Paris VI and CNRS, France) Patrizia Donato (Professor, University of Rouen, France) Klappentext 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. Zusammenfassung The theory of homogenization replaces a real composite material with an imaginary homogeneous one, to describe the macroscopic properties of the composite using the properties of the microscopic structure. This work illustrates the relevant mathematics, logic and methodology with examples. Inhaltsverzeichnis 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 ...

Product details

• Authors: D. Cioranescu, Diona Cioranescu, Doina Cioranescu, Doina (Directeur De Recherche Cioranescu, Doina Donato Cioranescu, Cioranescu Doina, Patrizia Donato, Patrizia (Professor Donato, Donato Patrizia
• Publisher: Oxford University Press
• Languages: English
• Product format: Hardback
• Released: 11.11.1999
• EAN: 9780198565543
• ISBN: 978-0-19-856554-3
• No. of pages: 272
• Series: Oxford Lecture Series in Mathematics and Its Applications; Oxford Lecture Series in Mathe; Oxford Lecture Series in Mathematics and Its Applications; Oxford Lecture Mathematics and
• Subjects: Natural sciences, medicine, IT, technology > Mathematics; SCIENCE / Mechanics / General, MATHEMATICS / Differential Equations / General, MATHEMATICS / Functional Analysis, MATHEMATICS / Calculus, Differential calculus & equations, Integral calculus & equations, Calculus of variations, Differential calculus and equations, Integral calculus and equations, Analytical mechanics