Geodesic
Secular condition for the McKean system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 44-48

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In this paper, we study the McKean kinetic system for two groups of particles with periodic initial data in the weight space. The system is reduced to an integro-differential operator containing nonintegrable terms. We find a secularity condition that allows one to eliminate the nondissipative part and hence reduce the problem to a nonlinear equation in a Hilbert space; this is the main step towards proving the stabilization of the solution.
Keywords: McKean kinetic system, Fourier series, weight space, Cauchy problem. 
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S. A. Dukhnovskii. Secular condition for the McKean system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 44-48. http://geodesic.mathdoc.fr/item/INTO_2023_220_a5/