Getting Acquainted with Homogenization and Multiscale
Authors: Berlyand, Leonid, Rybalko, Volodymyr
Free Preview- Development of an intuitive understanding that complements rigorous mathematics
- Makes advanced mathematical tools and concepts accessible to non-experts
- Presentations in all Chapters is supplied with exercises
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- About this Textbook
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The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.
- About the authors
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Leonid Berlyand is a Professor of Mathematics, and a member of the Materials Research Institute and Huck Institutes for Life Sciences at the Pennsylvania State University (USA) as well as an Honorary Professor (Professoris Honoris Cavza) at the Moscow State University. Leonid Berlyand is an internationally recognized expert in applied mathematics. He has made fundamental contributions to homogenization theory, mathematical Ginzburg-Landau theory, and mathematical biology.
Volodymyr Rybalko works as a senior research fellow in Mathematical Division, B.Verkin Institute for Low Temperature Physics and Engineering of National Academy of Sciences of Ukraine. He is an expert in the area of PDEs, he is known, in particular, for his contributions in homogenization theory.
- Table of contents (11 chapters)
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Preliminaries
Pages 1-15
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What Is Homogenization and Multiscale? First Examples
Pages 17-33
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Brief History and Surprising Examples in Homogenization
Pages 35-43
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Formal Two-Scale Asymptotic Expansions and the Corrector Problem
Pages 45-52
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Compensated Compactness and Oscillating Test Functions
Pages 53-58
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Table of contents (11 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Getting Acquainted with Homogenization and Multiscale
- Authors
-
- Leonid Berlyand
- Volodymyr Rybalko
- Series Title
- Compact Textbooks in Mathematics
- Copyright
- 2018
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-01777-4
- DOI
- 10.1007/978-3-030-01777-4
- Softcover ISBN
- 978-3-030-01776-7
- Series ISSN
- 2296-4568
- Edition Number
- 1
- Number of Pages
- XVIII, 178
- Number of Illustrations
- 28 b/w illustrations, 14 illustrations in colour
- Topics
