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Existence and Convergence to Equilibrium of a Kinetic Model for Cometary Flows

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Abstract

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on moments of the distribution function. An earlier existence result is extended to bounded domains with reflecting boundaries and to initial conditions permitting vacuum regions. The long time behaviour is investigated. Convergence on compact time intervals (shifted to infinity) to the set of equilibrium solutions is proven. The set of smooth equilibrium solutions is computed.

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Authors and Affiliations

  1. TU Wien, Institut für Angewandte und Numerische Mathematik, Wiedner Hauptstraße 8–10, A-1040, Wien, Austria

    Klemens Fellner & Christian Schmeiser

  2. UMR CNRS 6621, UNSA, Laboratoire J. A. Dieudonné, Parc Valrose, F-06108, Nice cedex 02, France

    Frederic Poupaud

Authors
  1. Klemens Fellner
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  2. Frederic Poupaud
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  3. Christian Schmeiser
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Fellner, K., Poupaud, F. & Schmeiser, C. Existence and Convergence to Equilibrium of a Kinetic Model for Cometary Flows. Journal of Statistical Physics 114, 1481–1499 (2004). https://doi.org/10.1023/B:JOSS.0000013956.08390.b1

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  • DOI: https://doi.org/10.1023/B:JOSS.0000013956.08390.b1

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