Entropy Methods for the Boltzmann Equation
Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
(Sprache: Englisch)
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or...
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Klappentext zu „Entropy Methods for the Boltzmann Equation “
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level.During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Inhaltsverzeichnis zu „Entropy Methods for the Boltzmann Equation “
- Entropy Production and Convergence to Equilibrium- Kinetic Limits for Interacting Particle Systems
Autoren-Porträt von Fraydoun Rezakhanlou, Cédric Villani
Cédric Villani, geboren 1973, gehört zu den weltweit führenden und innovativsten Mathematikern. Für seine Forschung erhielt er mehrere Preise, u.a. 2010 die renommierte Fields-Medaille, das Äquivalent zum Nobelpreis. Villani ist Professor für Mathematik an der École Normale Supérieure in Lyon und Direktor des Institut Henri Poincaré in Paris.
Bibliographische Angaben
- Autoren: Fraydoun Rezakhanlou , Cédric Villani
- 2007, XII, 113 Seiten, Masse: 15,9 x 23,8 cm, Kartoniert (TB), Englisch
- Herausgegeben: François Golse, Stefano Olla
- Verlag: Springer, Berlin
- ISBN-10: 3540737049
- ISBN-13: 9783540737049
- Erscheinungsdatum: 14.11.2007
Sprache:
Englisch
Rezension zu „Entropy Methods for the Boltzmann Equation “
From the reviews:"This nice book is based on two courses given, respectively, by Fraydoun Rezakhanlou and Cédric Villani at the Centre Émile Borel of the Institut Henri Poincaré in a special semester organized in the fall term of 2001 by Francois Golse and Stefano Olla. ... discusses many extensions, open questions and perspectives which should be valuable for many researchers in the field of the Boltzmann equation. ... This book ... will be useful to all mathematicians interested in entropy methods." (Clément Mouhot, Mathematical Reviews, Issue 2010 h)
Pressezitat
From the reviews: "This nice book is based on two courses given, respectively, by Fraydoun Rezakhanlou and Cédric Villani at the Centre Émile Borel of the Institut Henri Poincaré in a special semester organized in the fall term of 2001 by Francois Golse and Stefano Olla. ... discusses many extensions, open questions and perspectives which should be valuable for many researchers in the field of the Boltzmann equation. ... This book ... will be useful to all mathematicians interested in entropy methods." (Clément Mouhot, Mathematical Reviews, Issue 2010 h)
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