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arXiv · 0903.2739

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

Thibaut Allemand·Giuseppe Toscani
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Abstract

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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Thibaut Allemand, Giuseppe Toscani. 2009-03-16. The grazing collision limit of Kac caricature of Bose-Einstein particles. https://doi.org/10.3233/asy-2011-1031

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