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Exact Solutions of the Boltzmann Equations with a Source

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Abstract

Exact solutions of a nonlinear Boltzmann kinetic equation with a source are constructed in the case of an isotropic distribution function and Maxwell model of isotropic scattering. These solutions are constructed with the use of an equivalence group such that one of its transformations uniquely identifies the class of the source functions that are linear in terms of the distribution function; moreover, the transformed equation has a zero right side. As a result, invariant solutions of the type of the Bobylev–Krook–Wu solutions can be explicitly found, in particular, those that admit physical interpretation.

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Authors and Affiliations

  1. Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Yu. N. Grigor’ev

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    Yu. N. Grigor’ev

  3. School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand

    S. V. Meleshko & A. Suriyawichitseranee

Authors
  1. Yu. N. Grigor’ev
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  2. S. V. Meleshko
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  3. A. Suriyawichitseranee
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Correspondence to Yu. N. Grigor’ev.

Additional information

Original Russian Text © Yu.N. Grigor’ev, S.V. Meleshko, A. Suriyawichitseranee.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 2, pp. 3–11, March–April, 2018.

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Grigor’ev, Y.N., Meleshko, S.V. & Suriyawichitseranee, A. Exact Solutions of the Boltzmann Equations with a Source. J Appl Mech Tech Phy 59, 189–196 (2018). https://doi.org/10.1134/S0021894418020013

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  • DOI: https://doi.org/10.1134/S0021894418020013

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