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On diffuse reflection at the boundary for the Boltzmann equation and related equations

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Abstract

The paper considers diffuse reflection at the boundary with nonconstant boundary temperature and unbounded velocities. The solutions obtained are proved to conserve mass at the boundary. After a preliminary study of the collisionless case, the main results obtained are existence for the Boltzmann equation in a “DiPerna-Lions framework” with the above boundary conditions in a bounded measure sense, and existence together with uniqueness for the BGK equation with Maxwellian diffusion on the boundary in anL ∞ framework.

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Authors and Affiliations

  1. Department of Mathematics, University of Göteberg and Chalmers University of Technology, 412 96, Göteborg, Sweden

    L. Arkeryd

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  1. L. Arkeryd
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  2. N. Maslova
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Arkeryd, L., Maslova, N. On diffuse reflection at the boundary for the Boltzmann equation and related equations. J Stat Phys 77, 1051–1077 (1994). https://doi.org/10.1007/BF02183152

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  • DOI: https://doi.org/10.1007/BF02183152

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