The General Theory of Homogenization: A Personalized Introduction

Tartar, Luc

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.

Details

Published by: Springer

Publication Date: 2009-12-21

Format: Paperback

ISBN-13: 9783642051944

DOI: 10.1007/978-3-642-05195-1

Dimensions: 235.0cm x155.0cm

Pages: 471.0