On Linear Hypocoercive BGK Models

  • Franz Achleitner
  • Anton ArnoldEmail author
  • Eric A. Carlen
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 162)


We study hypocoercivity for a class of linear and linearized BGK models for discrete and continuous phase spaces. We develop methods for constructing entropy functionals that prove exponential rates of relaxation to equilibrium. Our strategies are based on the entropy and spectral methods, adapting Lyapunov’s direct method (even for “infinite matrices” appearing for continuous phase spaces) to construct appropriate entropy functionals. Finally, we also prove local asymptotic stability of a nonlinear BGK model.


Kinetic equations BGK models Hypocoercivity Entropy method 



The second author (AA) was supported by the FWF-doctoral school “Dissipation and dispersion in non-linear partial differential equations”. The third author (EC) was partially supported by U.S. N.S.F. grant DMS 1501007.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Franz Achleitner
    • 1
  • Anton Arnold
    • 1
    Email author
  • Eric A. Carlen
    • 2
  1. 1.Vienna University of TechnologyInstitute of Analysis and Scientific ComputingWienAustria
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA

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