Abstract:
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, equivalence group, gas dynamics equation.
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