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On a boundary layer problem for the nonlinear Boltzmann equation

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Abstract

This article deals with a boundary-layer problem arising in the kinetic theory of gases when the mean free path of molecules tends to zero. The model considered here is the stationary, nonlinear Boltzmann equation in one dimension with a slightly perturbed reflection boundary condition. We restrict our attention to the case of hard spheres collisions, with Grad's cutoff assumption. Existence, uniqueness and asymptotic behavior are derived by means of energy estimates.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées, Ecole Normale Supérieure, Paris

    Francois Golse, Benoit Perthame & Catherine Sulem

  2. Department of Mathematics, Ben Gurion University, Beer Sheva, Israel

    Francois Golse, Benoit Perthame & Catherine Sulem

Authors
  1. Francois Golse
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  2. Benoit Perthame
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  3. Catherine Sulem
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Communicated by Haim Brezis

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Golse, F., Perthame, B. & Sulem, C. On a boundary layer problem for the nonlinear Boltzmann equation. Arch. Rational Mech. Anal. 103, 81–96 (1988). https://doi.org/10.1007/BF00292921

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  • DOI: https://doi.org/10.1007/BF00292921

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