A GLOBAL EXISTENCE THEOREM FOR THE INITIAL-BOUNDARY-VALUE PROBLEM FOR THE BOLTZMANN-EQUATION WHEN THE BOUNDARIES ARE NOT ISOTHERMAL

We extend the existence theorem recently proved by HAMDACHE for the initial-boundary-value problem for the nonlinear Boltzmann equation in a vessel with isothermal boundaries to more general situations including the case when the boundaries are not isothermal. In the latter case a cut-off for large speeds is introduced in the collision term of the Boltzmann equation.