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2010, Volume 3, Issue 1: 1-15. Doi: 10.3934/krm.2010.3.1
This issue Previous Article Preface Next Article Flame structure from a kinetic model for chemical reactions

Small velocity and finite temperature variations in kinetic relaxation models

  • 1.

    Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501

  • 2.

    Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Wien

  • 3.

    Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA

Received:  December 2009
Revised:  December 2009
Published:  March 2010
Abstract Related Papers Cited by
    Abstract
  • 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.

    Citation:
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