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Field name	Details
Dewey Class	515.353
Title	The General Theory of Homogenization ([Ebook]) : A Personalized Introduction / by Luc Tartar.
Author	Tartar, Luc
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2010.
Physical Details	XXII, 471 pages : online resource.
Series	Lecture Notes of the Unione Matematica Italiana 1862-9113 ; ; 7
ISBN	9783642051951
Summary Note	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.:
Contents note	1 Why Do I Write?- 2 A Personalized Overview of Homogenization I -- 3 A Personalized Overview of Homogenization II -- 4 An Academic Question of Jacques-Louis Lions -- 5 A Useful Generalization by Francois Murat -- 6 Homogenization of an Elliptic Equation -- 7 The Div-Curl Lemma -- 8 Physical Implications of Homogenization -- 9 A Framework with Differential Forms -- 10 Properties of H-convergence -- 11 Homogenization of Monotone Operators -- 12 Homogenization of Laminated Materials -- 13 Correctors in Linear Homogenization -- 14 Correctors in Nonlinear Homogenization -- 15 Holes with Dirichlet Conditions -- 16 Holes with Neumann Conditions -- 17 Compensated Compactness -- 18 A Lemma for Studying Boundary Layers -- 19 A Model in Hydrodynamics -- 20 Problems in Dimension N = 2 -- 21 Bounds on Effective Coefficients -- 22 Functions Attached to Geometries -- 23 Memory Effects -- 24 Other Nonlocal Effects -- 25 The Hashin-Shtrikman Construction -- 26 Confocal Ellipsoids and Spheres -- 27 Laminations Again, and Again -- 28 Wave Front Sets, H-Measures -- 29 Small-Amplitude Homogenization -- 30 H-Measures and Bounds on Effective Coeffcients -- 31 H-Measures and Propagation Effects -- 32 Variants of H-Measures -- 33 Relations Between Young Measures and H-Measures -- 34 Conclusion -- 35 Biographical Information -- 36 Abbreviations and Mathematical Notation.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-05195-1
Links to Related Works	Subject References: Differential equations, Partial . Engineering Fluid Dynamics . Hydraulic engineering . Mathematics . Mechanics . Partial differential equations . Authors: Tartar, Luc . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes of the Unione Matematica Italiana . Classification: 515.353 .

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The General Theory of Homogenization: A Personalized Introduction

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