Descript 
1 online resource (xviii, 178 pages) : illustrations (some color), digital ; 24 cm 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 

text file PDF rda 
Series 
Compact textbooks in mathematics, 22964568


Compact textbooks in mathematics

Note 
Chapter 1 Preliminaries  Chapter 2 What is Homogenization and Multiscale? First Examples  Chapter 3 Brief History and Surprising Examples in Homogenization  Chapter 4 Formal Twoscale Asymptotic Expansions and the Corrector Problem  Chapter 5 Compensated Compactness and Oscillating Testfunctions  Chapter 6 Twoscale Convergence  Chapter 7 Examples of Explicit Effective Coefficients: Laminated Structures and 2D Checkerboards  Chapter 8 Introduction to Stochastic Homogenization  Chapter 9 GConvergence 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 

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 twoscale 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 nonmathematical students 
Host Item 
Springer eBooks

Subject 
Homogenization (Differential equations)


Multiscale modeling


Computational Science and Engineering


Mathematical and Computational Engineering


Partial Differential Equations

Alt Author 
Rybalko, Volodymyr, author


SpringerLink (Online service)

