Problem of evaporation-condensation for a two component gas in the slab

This paper studies the non linear Boltzmann equation for a two component gas in the situation of hard spheres. A Hilbert expansion of the solution is performed. The first order of the fluid equations shows the ghost effect. The fluid system is solved when the boundary conditions are close to each other.
    The boundary conditions for the kinetic system are satisfied by adding for the first and the second order Knudsen layers. In a last part the rest term is rigorously controled by using a decomposition into a low part velocity and a high part velocity. This constitutes a generalization to the case of a two component gas of the results presented in [15,16].