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arXiv · 1905.08873

Group analysis of the one-dimensional Boltzmann equation

A. V. Borovskikh·K. S. Platonova
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Abstract

The one-dimensional Boltzmann equation $f_{t} + cf_{x} + (\mathcal {F} f)_{c} = 0$ is considered with the function $\mathcal{F}$ depending on $(t, x, c, f)$. In this paper we obtain a complete group classification of such equations in the class of point transformations of the entire set of variables $(t, x, c, f)$ under the conditions of invariance of a) the relations $dx = cdt$, $dc = \mathcal {F} dt$, b) the lines $ dt = dx = 0 $ and c) the form $fdxdc$ fixing the physical meaning of the variables and the relationships between them.

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A. V. Borovskikh, K. S. Platonova. 2019-05-21. Group analysis of the one-dimensional Boltzmann equation. https://arxiv.org/abs/1905.08873

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