Geodesic
Group analysis of the one-dimensional Boltzmann equation: IV. Complete group classification in the general case
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 232-265
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We consider the one-dimensional Boltzmann equation $f_t+cf_x+(\mathcal{F} f)_c=0$ with a function $\mathcal{F}$ depending on $(t,x,c,f)$ and obtain the complete group classification of such equations in the class of point changes of whole set of variables $(t,x,c,f)$. For this, we impose additional conditions on the transformations for the invariance of (a) the relations $dx=c\,dt$ and $dc=\mathcal{F}\,dt$, (b) the lines $dt=dx=0$, and (c) the form $f\,dx\,dc$, which fix the physical meaning of the used variables and the relations between them.
Keywords: Boltzmann equation, symmetry group, gas dynamics equation.
Mots-clés : equivalence group 
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A. V. Borovskikh; K. S. Platonova. Group analysis of the one-dimensional Boltzmann equation: IV. Complete group classification in the general case. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 232-265. http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a6/

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