Global existence for two-velocity models of the Boltzmann equation

If A is a symmetric 2 × 2-matrix, then the initial value problem describes the evolution in time of a fictive gas whose particles can move only with the velocities u₁ and v₂. It is proved that, for continuous initial values vanishing at infinity, (1) has a global solution if an H-Theorem holds for the gas described by (1). The validity of an H-Theorem is expressed by the properties of A.