By Luc Tartar
Homogenization isn't really approximately periodicity, or Gamma-convergence, yet approximately knowing which powerful equations to take advantage of at macroscopic point, realizing which partial differential equations govern mesoscopic degrees, with out utilizing chances (which break actual reality); as a substitute, one makes use of a number of topologies of vulnerable kind, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the writer, and a few liable for the looks of nonlocal results, which many theories in continuum mechanics or physics guessed wrongly.
For a greater knowing of twentieth century technology, new mathematical instruments needs to be brought, just like the author’s H-measures, variations through Patrick Gérard, and others but to be came upon.
Read or Download The General Theory of Homogenization: A Personalized Introduction: 7 (Lecture Notes of the Unione Matematica Italiana) PDF
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The General Theory of Homogenization: A Personalized Introduction: 7 (Lecture Notes of the Unione Matematica Italiana) by Luc Tartar