On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model

For a stationary nonlinear Boltzmann equation in a slab with a particular trun-cation in the collision operator, the Milne problem for the boundary layer together with a weak type of hydrodynamic behavior in the interior of the slab are studied by nonperturbative methods in the small-mean-free-path limit. KEY WORDS: Boltzmann asymptotics; boundary layer; hydrodynamic limit; Maxwellian limit; Milne problem; stationary gas kinetics; weak methods