rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: General Theory of Homogenization
    sub title: A Personalized Introduction
  name:
    name part: Tartar, Luc.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXII, 471 p. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Luc Tartar.
  subject:
    topic: Physics
  subject:
    topic: Partial differential equations
  subject:
    topic: Mechanics
  subject:
    topic: Fluid mechanics
  subject:
    topic: Physics
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Mechanics
  subject:
    topic: Engineering Fluid Dynamics
  classification: QC19.2-20.85
  classification: 530.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes of the Unione Matematica Italiana, 7
  identifier: 9783642051951
  identifier: http://dx.doi.org/10.1007/978-3-642-05195-1
  record info:
    record creation date: 100301
    record change date: 20151204171713.0
    record identifier: 978-3-642-05195-1