The stationary Boltzmann equation for a two-component gas for soft forces in the slab

摘要

The stationary Boltzmann equation for soft forces in the context of a two-component gas is considered in the slab. An existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries in a renormalized sense. Weak L1 compactness is extracted from the control of the entropy production term. Trace at the boundaries is also controlled.