000 03645nam a22004815i 4500
001 978-3-642-05195-1
003 DE-He213
005 20140220084528.0
007 cr nn 008mamaa
008 100301s2010 gw | s |||| 0|eng d
020 _a9783642051951
_9978-3-642-05195-1
024 7 _a10.1007/978-3-642-05195-1
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aTartar, Luc.
_eauthor.
245 1 4 _aThe General Theory of Homogenization
_h[electronic resource] :
_bA Personalized Introduction /
_cby Luc Tartar.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXXII, 471p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes of the Unione Matematica Italiana,
_x1862-9113 ;
_v7
505 0 _aWhy 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 François Murat -- Homogenization of an Elliptic Equation -- The Div–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–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.
520 _aHomogenization 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.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aMechanics.
650 0 _aHydraulic engineering.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aMechanics.
650 2 4 _aEngineering Fluid Dynamics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642051944
830 0 _aLecture Notes of the Unione Matematica Italiana,
_x1862-9113 ;
_v7
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-05195-1
912 _aZDB-2-SMA
999 _c111692
_d111692