K. Aoki, A. Jüngel, P. Markowich:

"Small velocity and finite temperature variations in kinetic relaxation models";

in: "ASC Report 46/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

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.

http://www.asc.tuwien.ac.at/preprint/2009/asc46x2009.pdf

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