Geodesic
Group analysis of the~one-dimensional Boltzmann equation: III.~Condition for the~moment quantities to be physically meaningful
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 451-482

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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
Mots-clés : equivalence group. 
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     author = {K. S. Platonova and A. V. Borovskikh},
     title = {Group analysis of the~one-dimensional {Boltzmann} equation: {III.~Condition} for the~moment quantities to be physically meaningful},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {451--482},
     publisher = {mathdoc},
     volume = {195},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a6/}
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K. S. Platonova; A. V. Borovskikh. Group analysis of the~one-dimensional Boltzmann equation: III.~Condition for the~moment quantities to be physically meaningful. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 451-482. http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a6/