Overview
- The first book presenting the Periodic Unfolding Method in detail, written by the three mathematicians who developed it
- Significantly clarifies and simplifies the approach of homogenization for partial differential problems
- Contains detailed theory, as well as numerous and varied examples of applications
Part of the book series: Series in Contemporary Mathematics (SCMA, volume 3)
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About this book
This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems.
Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV). The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III). A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V). Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI).
This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.
Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV). The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III). A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V). Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI).
This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.
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Table of contents (15 chapters)
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Front Matter
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Unfolding in Fixed Domains
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Front Matter
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Unfolding in Perforated Domains
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Front Matter
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Partial Unfolding
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Front Matter
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Unfolding for small obstacles and strange terms
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Front Matter
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Linear Elasticity
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Front Matter
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An application: sharp error estimates
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Front Matter
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Authors and Affiliations
Bibliographic Information
Book Title: The Periodic Unfolding Method
Book Subtitle: Theory and Applications to Partial Differential Problems
Authors: Doina Cioranescu, Alain Damlamian, Georges Griso
Series Title: Series in Contemporary Mathematics
DOI: https://doi.org/10.1007/978-981-13-3032-2
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-3031-5Published: 13 November 2018
eBook ISBN: 978-981-13-3032-2Published: 03 November 2018
Series ISSN: 2364-009X
Series E-ISSN: 2364-0103
Edition Number: 1
Number of Pages: XV, 515
Number of Illustrations: 1 b/w illustrations
Topics: Partial Differential Equations, Theoretical and Applied Mechanics