Geodesic
Group analysis of the McKean system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 153-157

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In this paper, we examine the kinetic McKean system for two groups of particles. The system represents the Boltzmann kinetic equation, in this model, the momentum and the energy are not conserved. Using methods of group analysis, we obtain a solution representing the density of gas particles. Similarly, exact solutions for other kinetic models can be found.
Keywords: kinetic system McKean, group analysis
Mots-clés : invariant solution 
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     title = {Group analysis of the {McKean} system},
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     publisher = {mathdoc},
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S. A. Dukhnovskii. Group analysis of the McKean system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 153-157. http://geodesic.mathdoc.fr/item/INTO_2024_232_a11/