000 | 03645nam a22004815i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/978-3-642-05195-1 _2doi |
|
050 | 4 | _aQA370-380 | |
072 | 7 |
_aPBKJ _2bicssc |
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072 | 7 |
_aMAT007000 _2bisacsh |
|
082 | 0 | 4 |
_a515.353 _223 |
100 | 1 |
_aTartar, Luc. _eauthor. |
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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. |
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300 |
_aXXII, 471p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aLecture Notes of the Unione Matematica Italiana, _x1862-9113 ; _v7 |
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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 |