The General Theory of Homogenization A Personalized Introduction

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Luc Tartar, "The General Theory of Homogenization: A Personalized Introduction"
English | 2009 | pages: 494 | ISBN: 3642051944 | PDF | 2,7 mb
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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