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

Abstract

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 two components are different. An $L^{1}$ existence theorem is proved when one component satisfies a given data 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 of the mixture.