Abstract
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).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 165, Proceedings of the IV International Scientific Conference “Actual Problems of Applied Mathematics,” Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, 2019.
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Dukhnovskii, S.A. On the Rate of Stabilization of Solutions to the Cauchy Problem for the Godunov–Sultangazin System with Periodic Initial Data. J Math Sci 259, 349–375 (2021). https://doi.org/10.1007/s10958-021-05623-9
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DOI: https://doi.org/10.1007/s10958-021-05623-9