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Getting acquainted with homogenization and multiscale

Author: Leonid Berlyand; Volodymyr Rybalko
Publisher: Cham, Switzerland : Birkhäuser, 2018.
Series: Compact textbooks in mathematics
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Leonid Berlyand; Volodymyr Rybalko
ISBN: 9783030017774 303001777X
OCLC Number: 1077476216
Description: 1 online resource (xviii, 178 pages) : illustrations (some color).
Contents: Chapter 1- Preliminaries --
Chapter 2- What is Homogenization and Multiscale? First Examples --
Chapter 3- Brief History and Surprising Examples in Homogenization --
Chapter 4- Formal Two-scale Asymptotic Expansions and the Corrector Problem --
Chapter 5- Compensated Compactness and Oscillating Test-functions --
Chapter 6- Two-scale Convergence --
Chapter 7- Examples of Explicit Effective Coefficients: Laminated Structures and 2D Checkerboards --
Chapter 8- Introduction to Stochastic Homogenization --
Chapter 9- G-Convergence in Nonlinear Homogenization Problems --
Chapter 10- An Example of a Nonlinear Problem: Homogenization of Plasticity and Limit Loads --
Chapter 11- Continuum Limits for Discrete Problems with Fine Scales --
References --
Appendix: Regular and Singular Perturbations and Boundary Layers --
Index.
Series Title: Compact textbooks in mathematics
Responsibility: Leonid Berlyand, Volodymyr Rybalko.

Abstract:

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  Read more...

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