Titlebook: Getting Acquainted with Homogenization and Multiscale; Leonid Berlyand,Volodymyr Rybalko Textbook 2018 Springer Nature Switzerland AG 2018

星球的光亮度

Preliminaries,s and facts about functional spaces are presented in more detail, especially those concerning Sobolev spaces. Special attention is also paid to the notion of weak convergence which plays a key role in homogenization theory. Since the book deals with PDEs, the chapter contains a minimal background on

Confess

懸掛

Brief History and Surprising Examples in Homogenization,d Lord Rayleigh in the 19th century. We proceed with discussion on modern homogenization theory which was born in the 1960s and is actively developing nowadays. We also describe some interesting and surprising results, such as the so-called strange term appearing in the homogenization of Dirichlet p

ORE

Formal Two-Scale Asymptotic Expansions and the Corrector Problem,cs. The case study conductivity problem is used to illustrate the method of two-scale asymptotic expansions. This method, which is based on the idea of separation of slow and fast variables, proved to be extremely efficient not only in homogenization problems but also in the variety of other applica

intolerance

Compensated Compactness and Oscillating Test Functions,ormal expansions can become rather cumbersome. This chapter is devoted to an alternative justification approach that is much simpler to implement. It is based on the use of specially chosen oscillating test functions in the weak formulation of the problem so that upon passing to the limit one obtain

contrast-medium

exostosis