K. Aoki, A. Jüngel, P. Markowich:
"Small velocity and finite temperature variations in kinetic relaxation models";
Kinetic and Related Models, 3 (2010), 1; S. 1 - 15.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
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

Kinetic equation; diffusive limit; Gibbs state

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