Getting Acquainted with Homogenization and Multiscale

• Main Authors: Berlyand, Leonid (Author, http://id.loc.gov/vocabulary/relators/aut), Rybalko, Volodymyr (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Compact Textbooks in Mathematics,
• Subjects: Computer mathematics.; Applied mathematics.; Engineering mathematics.; Partial differential equations.; Computational Science and Engineering.; Mathematical and Computational Engineering.; Partial Differential Equations.

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...

Table of 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.