Planar boundary value problems for rarefied gases

A mathematically precise method is developed for solving planar boundary value problems for the nonlinear Boltzmann equation at a small Knudsen number. The method uses the exact solution of the linearized Milne and Kramers problems. That solution is valid in a boundary layer and is matched to a continuum solution that comes from the Chapman-Enskog expansion. The method is applied to two particular problems: a vapor layer between two liquids and a thermal-buoyant layer. A review is given of previous work on the vapor layer. In addition, a related method is used to describe the solution at the cold end of an infinitely strong shock. At the cold end the temperature is nearly zero and the molecular distribution is nearly a delta-function.