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Small velocity and finite temperature variations in kinetic relaxation models

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  • 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.
    Mathematics Subject Classification: Primary: 82C40, 35B40, 45K05; Secondary: 35M10.


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