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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Tartar, Luc (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2010.
Edición:1st ed. 2010.
Colección:Lecture Notes of the Unione Matematica Italiana, 7
Temas:
Mathematical physics.
Differential equations.
Mechanics.
Fluid mechanics.
Theoretical, Mathematical and Computational Physics.
Differential Equations.
Classical Mechanics.
Engineering Fluid Dynamics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Why Do I Write?
  • A Personalized Overview of Homogenization I
  • A Personalized Overview of Homogenization II
  • An Academic Question of Jacques-Louis Lions
  • A Useful Generalization by Fran#x00E7;ois Murat
  • Homogenization of an Elliptic Equation
  • The Div#x2013;Curl Lemma
  • Physical Implications of Homogenization
  • A Framework with Differential Forms
  • Properties of H-Convergence
  • Homogenization of Monotone Operators
  • Homogenization of Laminated Materials
  • Correctors in Linear Homogenization
  • Correctors in Nonlinear Homogenization
  • Holes with Dirichlet Conditions
  • Holes with Neumann Conditions
  • Compensated Compactness
  • A Lemma for Studying Boundary Layers
  • A Model in Hydrodynamics
  • Problems in Dimension = 2
  • Bounds on Effective Coefficients
  • Functions Attached to Geometries
  • Memory Effects
  • Other Nonlocal Effects
  • The Hashin#x2013;Shtrikman Construction
  • Confocal Ellipsoids and Spheres
  • Laminations Again, and Again
  • Wave Front Sets, H-Measures
  • Small-Amplitude Homogenization
  • H-Measures and Bounds on Effective Coefficients
  • H-Measures and Propagation Effects
  • Variants of H-Measures
  • Relations Between Young Measures and H-Measures
  • Conclusion
  • Biographical Information
  • Abbreviations and Mathematical Notation.

Ejemplares similares