Getting Acquainted with Homogenization and Multiscale

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 tw...

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Hlavní autor: Berlyand, Leonid (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Cham : Springer International Publishing, 2018.
Vydání:1st ed. 2018.
Edice:Compact Textbooks in Mathematics,
Témata:
Computer mathematics.
Applied mathematics.
Engineering mathematics.
Partial differential equations.
ISBN:9783030017774
ISSN:2296-4568
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Obsah:
  • 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.

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