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The General Theory of Homogenization A Personalized Introduction /

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...

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Bibliographic Details
Main Author: Tartar, Luc. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
Series:Lecture Notes of the Unione Matematica Italiana, 7
Subjects:
Mathematics.
Differential equations, partial.
Mechanics.
Hydraulic engineering.
Partial Differential Equations.
Engineering Fluid Dynamics.
Online Access:https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-05195-1
Table of Contents:
  • 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.

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