Long-time behaviour of a one-dimensional BGK model: convergence to macroscopic rarefaction waves

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• 作者：Carlota Maria Cuesta (1)
  C. Schmeiser (2) (3)
  
• 关键词：BGK type kinetic model ; Relaxation to conservation laws ; Rarefaction waves ; 35Q99 ; 35B40 ; 35L99 ; 76P05
• 刊名：Monatshefte f眉r Mathematik
• 出版年：2010
• 出版时间：July 2010
• 年：2010
• 卷：160
• 期：4
• 页码：361-374
• 全文大小：179KB
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• 作者单位：Carlota Maria Cuesta (1)
  C. Schmeiser (2) (3)
  
  1. Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, NG7 2RD, Nottingham, UK
  2. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090, Vienna, Austria
  3. Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria
  
• ISSN：1436-5081

文摘

For one-dimensional kinetic BGK models, regarded as relaxation models for scalar conservation laws with genuinely nonlinear fluxes, we prove that the macroscopic density converges to the rarefaction wave solution of the corresponding scalar conservation law in the long time limit, and that the phase space density approaches an equilibrium distribution with the rarefaction wave as macroscopic density. The proof requires a smallness assumption on the amplitude of the rarefaction waves and uses a micro-macro decomposition of the perturbation equation.