G-Convergence and Homogenization of Nonlinear Partial Differential Operators / Edition 1

G-Convergence and Homogenization of Nonlinear Partial Differential Operators / Edition 1

by A.A. Pankov
     
 

This volume deals with G-convergence and homogenization for various classes of nonlinear partial differential operators. Chapter 1 is devoted to some preliminary issues from nonlinear analysis as well as to G-convergence of abstract operators, including the case of abstract parabolic operators. Chapter 2 introduces details of the notion of strong G-convergence for

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Overview

This volume deals with G-convergence and homogenization for various classes of nonlinear partial differential operators. Chapter 1 is devoted to some preliminary issues from nonlinear analysis as well as to G-convergence of abstract operators, including the case of abstract parabolic operators. Chapter 2 introduces details of the notion of strong G-convergence for nonlinear second order elliptic operators in divergence form, and in Chapter 3 the homogenization problem for rapidly oscillated nonlinear random homogenous elliptic operators is dealt with. On the basis of these results, almost periodic and periodic cases are studied. Finally, in Chapter 4, some of the previous results are extended to the case of nonlinear parabolic operators. The volume concludes with two appendices, one of which is devoted to homogenization of nonlinear difference schemes, while the other lists some open problems of relevance, and a bibliography.
Audience: This work will be of interest to researchers whose work involves homogenization theory and its applications. It is also recommended for advanced courses in the fields of partial differential equations and nonlinear analysis.

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Product Details

ISBN-13:
9780792347200
Publisher:
Springer Netherlands
Publication date:
09/30/1997
Series:
Mathematics and Its Applications (closed) Series, #422
Edition description:
1997
Pages:
258
Product dimensions:
9.21(w) x 6.14(h) x 0.69(d)

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Table of Contents

Preface
Notations
1G-convergence of Abstract Operators1
2Strong G-convergence of Nonlinear Elliptic Operators45
3Homogenization of Elliptic Operators131
4Nonlinear Parabolic Operators173
AHomogenization of Nonlinear Difference Schemes213
BOpen Problems224
References229
Index248

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