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Asymptotic Analysis for Periodic Structures

A. Bensoussan University of Texas at Dallas, Richardson, TX and Hong Kong Polytechnic University, Kowloon, Hong Kong
G. Papanicolaou Stanford University, Stanford, CA
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN: 978-0-8218-5324-5
Product Code: CHEL/374.H
List Price: $61.00 MAA Member Price:$54.90
AMS Member Price: $54.90 Electronic ISBN: 978-1-4704-1581-5 Product Code: CHEL/374.H.E List Price:$61.00
MAA Member Price: $54.90 AMS Member Price:$48.80
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AMS Member Price: $82.35 Click above image for expanded view Asymptotic Analysis for Periodic Structures A. Bensoussan University of Texas at Dallas, Richardson, TX and Hong Kong Polytechnic University, Kowloon, Hong Kong G. Papanicolaou Stanford University, Stanford, CA AMS Chelsea Publishing: An Imprint of the American Mathematical Society Available Formats:  Hardcover ISBN: 978-0-8218-5324-5 Product Code: CHEL/374.H  List Price:$61.00 MAA Member Price: $54.90 AMS Member Price:$54.90
 Electronic ISBN: 978-1-4704-1581-5 Product Code: CHEL/374.H.E
 List Price: $61.00 MAA Member Price:$54.90 AMS Member Price: $48.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$91.50 MAA Member Price: $82.35 AMS Member Price:$82.35
• Book Details

AMS Chelsea Publishing
Volume: 3741978; 392 pp
MSC: Primary 80; 35; 74; 60;

This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization.

In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.

Graduate students and research mathematicians interested in asymptotic and probabilistic methods in the analysis of partial differential equations.

• Chapters
• Introduction
• Chapter 1. Elliptic operators
• Chapter 2. Evolution operators
• Chapter 3. Probabilistic problems and methods
• Chapter 4. High frequency wave propagation in periodic structures

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Volume: 3741978; 392 pp
MSC: Primary 80; 35; 74; 60;

This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization.

In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.