The General Theory of Homogenization A Personalized Introduction /

• Main Author: Tartar, Luc (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Lecture Notes of the Unione Matematica Italiana, 7
• Subjects: Physics.; Partial differential equations.; Mechanics.; Fluid mechanics.; Theoretical, Mathematical and Computational Physics.; Partial Differential Equations.; Engineering Fluid Dynamics.
• Physical Description: XXII, 471 p. online resource.
• ISBN: 9783642051951
• ISSN: 1862-9113 ;

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.