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Equilibrium Solution to the Inelastic Boltzmann Equation Driven by a Particle Bath

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Abstract

We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host medium with a fixed distribution. This is achieved by controlling the L p-norms, the moments and the regularity of the solutions to the Cauchy problem together with arguments related to a dynamical proof for the existence of stationary states.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, 43100, Parma, Italy

    Marzia Bisi

  2. ICREA (Institució Catalana de Recerca i Estudis Avançats) and Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    José A. Carrillo

  3. Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand 2), 63177, Aubière Cedex, France

    Bertrand Lods

Authors
  1. Marzia Bisi
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  2. José A. Carrillo
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  3. Bertrand Lods
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Correspondence to Marzia Bisi.

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Bisi, M., Carrillo, J.A. & Lods, B. Equilibrium Solution to the Inelastic Boltzmann Equation Driven by a Particle Bath. J Stat Phys 133, 841–870 (2008). https://doi.org/10.1007/s10955-008-9636-6

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  • DOI: https://doi.org/10.1007/s10955-008-9636-6

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