Small velocity and finite temperature variations in kinetic relaxation models | Zendy

Kazuo Aoki | Zendy; Ansgar Jüngel | Zendy; Peter A. Markowich | Zendy

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Small velocity and finite temperature variations in kinetic relaxation models

Author(s) -

Kazuo Aoki,

Ansgar Jüngel,

Peter A. Markowich

Publication year - 2010

Publication title -

kinetic and related models

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.987

H-Index - 28

eISSN - 1937-5093

pISSN - 1937-5077

DOI - 10.3934/krm.2010.3.1

Subject(s) - knudsen number , statistical physics , kinetic energy , collision , kinetic theory , relaxation (psychology) , physics , boltzmann equation , kernel (algebra) , mathematics , mathematical analysis , classical mechanics , mechanics , thermodynamics , computer science , psychology , social psychology , computer security , combinatorics

A small Knuden number analysis of a kinetic equation in the diffusive scaling is performed. The collision kernel is of BGK type with a general local Gibbs state. Assuming that the flow velocity is of the order of the Knudsen number, a Hilbert expansion yields a macroscopic model with finite temperature variations, whose complexity lies in between the hydrodynamic and the energy-transport equations. Its mathematical structure is explored and macroscopic models for specific examples of the global Gibbs state are presented. © American Institute of Mathematical Sciences

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