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100301s2010 gw | s |||| 0|eng d |
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|a 9783642051951
|9 978-3-642-05195-1
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|a 10.1007/978-3-642-05195-1
|2 doi
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|a QA370-380
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|a MAT007000
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|a 515.353
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|a Tartar, Luc.
|e author.
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|a The General Theory of Homogenization
|b A Personalized Introduction /
|c by Luc Tartar.
|h [electronic resource] :
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg,
|c 2010.
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|a XXII, 471p.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
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|a text file
|b PDF
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|a Lecture Notes of the Unione Matematica Italiana,
|v 7
|x 1862-9113 ;
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|a 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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|a 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 Franȯis 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<U+0019>s H-measures, variants by Patrick Gřard, and others yet to be discovered.
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|a Mathematics.
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|a Differential equations, partial.
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|a Mechanics.
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|a Hydraulic engineering.
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|a Mathematics.
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|a Partial Differential Equations.
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| 650 |
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|a Mechanics.
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|a Engineering Fluid Dynamics.
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| 710 |
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783642051944
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| 830 |
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|a Lecture Notes of the Unione Matematica Italiana,
|v 7
|x 1862-9113 ;
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|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-05195-1
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|a ZDB-2-SMA
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| 950 |
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|a Mathematics and Statistics (Springer-11649)
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