Geodesic
On the rate of stabilization of solutions to the Cauchy problem for the Godunov–Sultangazin system with periodic initial data
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 88-113

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In this paper, we examine a one-dimensional system of equations for a discrete gas model (the Godunov–Sultangazin system). The Godunov–Sultangazin system is the Boltzmann kinetic equation for a model one-dimensional gas consisting of three groups of particles. In this model, the momentum is preserved whereas the energy is not. We prove the existence of a unique global solution to the Cauchy problem for a perturbation of the equilibrium state with periodic initial data. For the first time, we find the rate of stabilization to the equilibrium state (exponential stabilization).
Keywords: Godunov–Sultangazin system, existence theorem, weak solution, Knudsen number. 
S. A. Dukhnovskii. On the rate of stabilization of solutions to the Cauchy problem for the Godunov–Sultangazin system with periodic initial data. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 88-113. http://geodesic.mathdoc.fr/item/INTO_2019_165_a8/
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     title = {On the rate of stabilization of solutions to the {Cauchy} problem for the {Godunov{\textendash}Sultangazin} system with periodic initial data},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {88--113},
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