Abstract
A method for solving kinetic boundary layer problems for the (1D) Klein-Kramers equation, the kinetic equation for Brownian particles, was proposed a few years ago by Marshall and Watson (1987) for the special case of particles moving under the influence of a constant or zero external force. In this paper the authors apply this method to a number of classical stationary boundary layer problems for completely or partially absorbing walls. These are the Milne problem, in which a current flows towards the wall from infinity, and the albedo problem, in which particles are injected into the system at the wall with a prescribed velocity distribution. The solutions are known to be non-analytic at the wall for zero normal velocity; the authors pay particular attention to the nature of this singularity for several special cases. The results are compared with results obtained by approximate methods.