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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