Global solution of the initial value problem for a discrete velocity model of the Boltzmann equation

The Broadwell model of the Boltzmann equation for a discrete velocity gas is the space regular model with six velocities.This model is investigated on the initial value problem.It is proved that a unique solution exists globally in time for the small initial data and that the solution has the bound which depends only on the initial data.A priori estimate for the solution is based on the mass conser- vation law.