The stationary Boltzmann equation for a two‐component gas in the slab

The stationary Boltzmann equation for hard forces in the context of a two‐component gas is considered in the slab. An L¹ existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak L¹ compactness is extracted from the control of the entropy production term. Trace at the boundaries are also controlled. Copyright © 2007 John Wiley & Sons, Ltd.