On the rate of stabilization of solutions to the Cauchy problem for the Godunov-Sultangazin system with periodic initial data
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).