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Existence and uniqueness for nonlinear boundary value problems in kinetic theory

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Abstract

A boundary value problem for the stationary nonlinear Boltzmann equation in a slab has been examined in a weightedL ∞ space. It has been proved that the problem possesses a unique solution for boundary data small enough. The proof is based on the implicit function theorem. It has also been shown that for the linearized problem the Fredholm alternative applies.

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Authors and Affiliations

  1. Dipartimento di Matematica del Politecnico di Milano, Milan, Italy

    Carlo Cercignani

  2. Department of Mathematics, University of Warsaw, Warsaw, Poland

    Andrzej Palczewski

Authors
  1. Carlo Cercignani
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  2. Andrzej Palczewski
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Cercignani, C., Palczewski, A. Existence and uniqueness for nonlinear boundary value problems in kinetic theory. J Stat Phys 46, 273–281 (1987). https://doi.org/10.1007/BF01010346

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  • DOI: https://doi.org/10.1007/BF01010346

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