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Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases

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Abstract

We consider the Boltzmann equation in the framework of a nonlinear model for problems of the gas flow in a half-space (the Kramers problem). We prove the existence of a positive bounded solution and find the limit of this solution at infinity. We show that taking the nonlinear dependence of the collision integral on the distribution function into account leads to an asymptotically new solution of the initial equation. To illustrate the result, we present examples of functions describing the nonlinearity of the collision integral.

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Authors and Affiliations

  1. Armenian State Agrarian University, Yerevan, Armenia

    A. Kh. Khachatryan

  2. Institute of Mathematics, Armenian National Academy of Sciences, Yerevan, Armenia

    Kh. A. Khachatryan

Authors
  1. A. Kh. Khachatryan
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  2. Kh. A. Khachatryan
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Correspondence to A. Kh. Khachatryan.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 3, pp. 497–504, September, 2012.

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Khachatryan, A.K., Khachatryan, K.A. Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases. Theor Math Phys 172, 1315–1320 (2012). https://doi.org/10.1007/s11232-012-0116-4

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  • DOI: https://doi.org/10.1007/s11232-012-0116-4

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