The grazing collision limit of Kac caricature of Bose-Einstein particles

Details The grazing collision limit of Kac caricature of Bose-Einstein particles The grazing collision limit of Kac caricature of Bose-Einstein particles

2009-03-16

arxiv.org/abs/0903.2739v3

Asymptotic Analysis 72, 3-4 (2011) 201-229

Mathematics

Analysis of PDEs

28 pages

Scientific paper

10.3233/ASY-2011-1031

We discuss the grazing collision limit of certain kinetic models of Bose-Einstein particles obtained from a suitable modification of the one- dimensional Kac caricature of a Maxwellian gas without cut-off. We recover in the limit a nonlinear Fokker-Planck equation which presents many similarities with the one introduced by Kaniadakis and Quarati in [13 ]. In order to do so, we perform a study of the moments of the solution. Moreover, as is typical in Maxwell models, we make an essential use of the Fourier version of the equation.

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