Global existence for two‐velocity models of the Boltzmann equation

If A is a symmetric 2 × 2‐matrix,then the initial value problemdescribes the evolution in time of a fictive gas whose particles can move only with the velocities u 1 and v 2 . 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 .