Geodesic
Secularity condition for the Broadwell kinetic system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 1, Tome 238 (2025), pp. 49-58.

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In this paper, we study the Broadwell kinetic system for four groups of particles with periodic initial data in a weight space. The solution is sought in a neighborhood of the equilibrium state. The perturbation is expanded in a Fourier series. Conditions for local equilibria for solutions of the Cauchy problem are found.
Keywords: Broadwell kinetic system, Fourier series, weighted space, Cauchy problem 
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S. A. Dukhnovskii. Secularity condition for the Broadwell kinetic system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 1, Tome 238 (2025), pp. 49-58. http://geodesic.mathdoc.fr/item/INTO_2025_238_a3/

[9] Vasileva O. A., Dukhnovskii S. A., Radkevich E. V., “O lokalnom ravnovesii uravneniya Karlemana”, Mezhvuz. sb. Probl. mat. anal., 78 (2015), 165–190 | Zbl

[10] Vasileva O. A., Dukhnovskii S. A., Radkevich E. V., “O prirode lokalnogo ravnovesiya uravnenii Karlemana i Godunova—Sultangazzina”, Sovr. mat. Fundam. napr., 60 (2016), 23–81

[11] Vedenyapin V. V., Mingalev I. V., Mingalev O. V., “O diskretnykh modelyakh kvantovogo uravneniya Boltsmana”, Mat. sb., 184:11 (1993), 21–38 | Zbl

[12] Godunov S. K., Sultangazin U. M., “O diskretnykh modelyakh kineticheskogo uravneniya Boltsmana”, Usp. mat. nauk., 26:3 (1971), 3–51 | MR | Zbl

[13] Dukhnovskii S. A., “Test Penleve i avtomodelnoe reshenie kineticheskoi modeli”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 176 (2020), 91–94 | DOI | MR

[14] Ilin O. V., “Statsionarnye resheniya kineticheskoi modeli Broduella”, Teor. mat. fiz., 170:3 (2012), 481–488 | DOI

[15] Lindblom O., Eiler N., “Reshenie uravnenii Boltsmana dlya diskretnykh skorostei pri pomoschi uravnenii Beitmena i Rikkati”, Teor. mat. fiz., 131:2 (2002), 179–193 | DOI | MR | Zbl

[16] Radkevich E. V., “O diskretnykh kineticheskikh uravneniyakh”, Dokl. Ross. Akad. nauk., 447:4 (2012), 369–373 | MR | Zbl

[17] Dukhnovsky S. A., “On solutions of the kinetic McKean system”, Bul. Acad. Ştiinţe Rep. Mold. Mat., 94:3 (2020), 3–11 | MR | Zbl

[18] Dukhnovsky S. A., “The tanh-function method and the $(G'/G)$-expansion method for the kinetic McKean system”, Differ. Equations Control Processes., 2021, no. 2, 87–100 | MR | Zbl

[19] Dukhnovsky S. A., “Secular terms for the kinetic McKean model”, Differ. Equations Control Processes., 2023, no. 1, 125–136 | DOI | MR | Zbl

[20] Euler N., Steeb W.-H., “Painlevé test and discrete Boltzmann equations”, Austr. J. Phys., 42 (1989), 1–10 | DOI | MR