Entropy methods for the Boltzmann equation: lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Lecture notes in mathematics
1916 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 107 S. graph. Darst. 24cm |
| ISBN: | 3540737049 9783540737049 |
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| 245 | 1 | 0 | |a Entropy methods for the Boltzmann equation |b lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 |c Fraydoun Rezakhanlou ; Cédric Villani |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XII, 107 S. |b graph. Darst. |c 24cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1916 | |
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| 650 | 4 | |a Transport, Théorie du | |
| 650 | 4 | |a Transport theory | |
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Datensatz im Suchindex
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Contents
1 Entropy Production and Convergence to Equilibrium 1
C. Villani
1.1 The Entropy Production Problem for the Boltzmann
Equation 1
1.1.1 The Boltzmann Equation: Notation and Preliminaries 1
1.1.2 H Functional and H Theorem 4
1.1.3 What this Course is About: Convergence
to Equilibrium 9
1.2 Tentative Panomara 11
1.3 Reminders from Information Theory 12
1.3.1 Background and Definitions 12
1.3.2 Inequalities 15
1.4 Quantitative H Theorem 18
1.4.1 Entropy Entropy Production Inequalities 18
1.4.2 EEP Inequalities for the Boltzmann Equation 19
1.4.3 Proof of Cercignani's Conjecture in a Special Case . 31
1.5 The State of the Art for the Spatially Homogeneous
Boltzmann Equation 32
1.5.1 Preparations 32
1.5.2 Current State of Regularity Theory 34
1.5.3 Convergence to Equilibrium 35
1.6 A Review of Some Closely Related Topics 37
1.6.1 Particles Systems and Kac's Problem 37
1.6.2 The Central Limit Theorem for Maxwellian
Molecules 44
1.6.3 The Role of High Energy Tails 48
1.6.4 Behavior of the Fisher Information 49
1.6.5 Variations on a Theme 50
1.7 Wiping out Spatial Inhomogeneities 51
1.8 Towards Exponential Convergence? 62
References 64
Appendix 69
xi
xii Contents
2 Kinetic Limits for Interacting Particle Systems 71
F. Rezakhanlou
2.1 Introduction 71
2.2 Equilibrium Fluctuations 80
2.3 Kinetic Limits in Dimension One 91
2.4 Kinetic Limits in Higher Dimensions 98
References 105
Index 107 |
| adam_txt |
Contents
1 Entropy Production and Convergence to Equilibrium 1
C. Villani
1.1 The Entropy Production Problem for the Boltzmann
Equation 1
1.1.1 The Boltzmann Equation: Notation and Preliminaries 1
1.1.2 H Functional and H Theorem 4
1.1.3 What this Course is About: Convergence
to Equilibrium 9
1.2 Tentative Panomara 11
1.3 Reminders from Information Theory 12
1.3.1 Background and Definitions 12
1.3.2 Inequalities 15
1.4 Quantitative H Theorem 18
1.4.1 Entropy Entropy Production Inequalities 18
1.4.2 EEP Inequalities for the Boltzmann Equation 19
1.4.3 Proof of Cercignani's Conjecture in a Special Case . 31
1.5 The State of the Art for the Spatially Homogeneous
Boltzmann Equation 32
1.5.1 Preparations 32
1.5.2 Current State of Regularity Theory 34
1.5.3 Convergence to Equilibrium 35
1.6 A Review of Some Closely Related Topics 37
1.6.1 Particles Systems and Kac's Problem 37
1.6.2 The Central Limit Theorem for Maxwellian
Molecules 44
1.6.3 The Role of High Energy Tails 48
1.6.4 Behavior of the Fisher Information 49
1.6.5 Variations on a Theme 50
1.7 Wiping out Spatial Inhomogeneities 51
1.8 Towards Exponential Convergence? 62
References 64
Appendix 69
xi
xii Contents
2 Kinetic Limits for Interacting Particle Systems 71
F. Rezakhanlou
2.1 Introduction 71
2.2 Equilibrium Fluctuations 80
2.3 Kinetic Limits in Dimension One 91
2.4 Kinetic Limits in Higher Dimensions 98
References 105
Index 107 |
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| isbn | 3540737049 9783540737049 |
| language | English |
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| spelling | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 Fraydoun Rezakhanlou ; Cédric Villani Berlin [u.a.] Springer 2008 XII, 107 S. graph. Darst. 24cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1916 Entropie Transport, Théorie du Transport theory Entropy Entropie (DE-588)4014894-4 gnd rswk-swf Boltzmann-Gleichung (DE-588)4146261-0 gnd rswk-swf Boltzmann-Gleichung (DE-588)4146261-0 s Entropie (DE-588)4014894-4 s DE-604 Rezakhanlou, Fraydoun Sonstige oth Villani, Cédric 1973- Sonstige (DE-588)13389701X oth Lecture notes in mathematics 1916 (DE-604)BV000676446 1916 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016234618&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 Lecture notes in mathematics Entropie Transport, Théorie du Transport theory Entropy Entropie (DE-588)4014894-4 gnd Boltzmann-Gleichung (DE-588)4146261-0 gnd |
| subject_GND | (DE-588)4014894-4 (DE-588)4146261-0 |
| title | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 |
| title_auth | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 |
| title_exact_search | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 |
| title_exact_search_txtP | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 |
| title_full | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 Fraydoun Rezakhanlou ; Cédric Villani |
| title_fullStr | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 Fraydoun Rezakhanlou ; Cédric Villani |
| title_full_unstemmed | Entropy methods for the Boltzmann equation lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 Fraydoun Rezakhanlou ; Cédric Villani |
| title_short | Entropy methods for the Boltzmann equation |
| title_sort | entropy methods for the boltzmann equation lectures from a special semester at the centre emile borel institut h poincare paris 2001 |
| title_sub | lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 |
| topic | Entropie Transport, Théorie du Transport theory Entropy Entropie (DE-588)4014894-4 gnd Boltzmann-Gleichung (DE-588)4146261-0 gnd |
| topic_facet | Entropie Transport, Théorie du Transport theory Entropy Boltzmann-Gleichung |
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