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© 2018

Getting Acquainted with Homogenization and Multiscale

Benefits

  • 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

Textbook

Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Leonid Berlyand, Volodymyr Rybalko
    Pages 1-15
  3. Leonid Berlyand, Volodymyr Rybalko
    Pages 17-33
  4. Leonid Berlyand, Volodymyr Rybalko
    Pages 35-43
  5. Leonid Berlyand, Volodymyr Rybalko
    Pages 45-52
  6. Leonid Berlyand, Volodymyr Rybalko
    Pages 53-58
  7. Leonid Berlyand, Volodymyr Rybalko
    Pages 59-74
  8. Leonid Berlyand, Volodymyr Rybalko
    Pages 85-101
  9. Leonid Berlyand, Volodymyr Rybalko
    Pages 103-122
  10. Leonid Berlyand, Volodymyr Rybalko
    Pages 139-168
  11. Back Matter
    Pages 169-178

About this book

Introduction

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.


Keywords

Multiscale Homogenization Effective coefficients Asymptotic expansion Gamma-convergence Two-scale convergence Continuum limit Stochastic homogenizaiton Cell problem Plasticity Composite material Heterogeneous media

Authors and affiliations

  1. 1.Mathematics and Materials Research InstitutePennsylvania State UniversityUniversity ParkUSA
  2. 2.Mathematical DivisionB Verkin Institute for Low Temperature Physics and Engineering of National Academy of Sciences of UkraineKharkivUkraine

About the authors

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. 


Bibliographic information

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Reviews

“This book is an invitation to the young researcher to start using modern asymptotic methods of the applied mathematics of multiscale systems.” (Adrian Muntean, zbMATH 1441.35001, 2020)