EAN: 9783540737049

ENTROPY METHODS FOR THE BOLTZMANN EQUATION - FR...

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.

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