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Equivalence group and exact solutions of the system of nonhomogeneous Boltzmann equations

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Abstract

The article is devoted to the construction of exact solutions of a system of two Boltzmann kinetic inhomogeneous equations. The source functions in the equations simulate the integrals of double and triple inelastic collisions. An extension of the Lie group \(L_4\) admitted by the system of homogeneous equations is carried out. In the present paper, the Lie group \(L_4\) is considered as an equivalence group for inhomogeneous equations. Conditions are found under which transformations from the extended group vanish the sources in the transformed equations. A class of sources linear in the distribution functions is obtained for which the generalized Bobylev–Krook–Wu solutions hold in explicit form. Physical interpretations are also presented.

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Acknowledgements

The research was supported by Russian Science Foundation Grant No. 23-11-00027.

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Author notes

  1. Yurii N. Grigoryev and Sergey V. Meleshko contributed equally to this work.

Authors and Affiliations

  1. Institute of Computational Technology, Novosibirsk, Russia, 630090

    Yurii N. Grigoryev

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

    Sergey V. Meleshko

Authors
  1. Yurii N. Grigoryev
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  2. Sergey V. Meleshko
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Correspondence to Sergey V. Meleshko.

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Communicated by Andreas Öchsner.

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Grigoryev, Y.N., Meleshko, S.V. Equivalence group and exact solutions of the system of nonhomogeneous Boltzmann equations. Continuum Mech. Thermodyn. 35, 2117–2124 (2023). https://doi.org/10.1007/s00161-023-01238-4

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  • DOI: https://doi.org/10.1007/s00161-023-01238-4

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