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. 
@article{INTO_2019_165_a8,
     author = {S. A. Dukhnovskii},
     title = {On the rate of stabilization of solutions to the {Cauchy} problem for the {Godunov--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},
     publisher = {mathdoc},
     volume = {165},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_165_a8/}
}
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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/