The Stationary Boltzmann equation for a two component gas in the slab with different molecular masses

The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An $L^1$ existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak $L^1$ compactness is extracted from the control of the entropy production term.