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Group Analysis of the One-Dimensional Boltzmann Equation: III. Condition for the Moment Quantities to Be Physically Meaningful

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Abstract

We present the group classification of the one-dimensional Boltzmann equation with respect to the function F = F(t, x, c) characterizing an external force field under the assumption that the physically meaningful constraints dx = c dt, dc = F dt, dt = 0, and dx =0 are imposed on the variables. We show that for all functions F, the algebra is finite-dimensional, and its maximum dimension is eight, which corresponds to the equation with a zero F.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    K. S. Platonova & A. V. Borovskikh

Authors
  1. K. S. Platonova
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  2. A. V. Borovskikh
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Corresponding author

Correspondence to K. S. Platonova.

Additional information

This research was supported by the Russian Foundation for Basic Research (Grant No. 15–01-04066).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 195, No. 3, pp. 451–482, June, 2018.

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Platonova, K.S., Borovskikh, A.V. Group Analysis of the One-Dimensional Boltzmann Equation: III. Condition for the Moment Quantities to Be Physically Meaningful. Theor Math Phys 195, 886–915 (2018). https://doi.org/10.1134/S0040577918060077

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  • DOI: https://doi.org/10.1134/S0040577918060077

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