ENGLISH

The General Theory of Homogenization: A Personalized Introduction

By Luc Tartar (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2010
ISBN
978-3-642-05194-4, 978-3-642-05195-1
DOI
10.1007/978-3-642-05195-1
Language
english
Format
PDF
Filesize
10 MB (10442796 bytes)
Series
Lecture Notes of the Unione Matematica Italiana 7
Edition
1
Pages
471\465
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Partial Differential Equations;Mechanics;Engineeri

Description

Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.

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