This article is cited in 6 papers

Group analysis of the one-dimensional Boltzmann equation: III. Condition for the moment quantities to be physically meaningful

K. S. Platonova, A. V. Borovskikh

Lomonosov Moscow State University

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

Keywords: Boltzmann equation, symmetry group, gas dynamics equation, equivalence group.

Received: 15.06.2017
Revised: 07.08.2017

DOI: 10.4213/tmf9425

 English version: Theoretical and Mathematical Physics, 2018, 195:3, 886–915

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