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

TL;DR

This paper proves an $L^{1}$ existence theorem for the stationary Boltzmann equation in a two-component gas with different molecular masses in a slab, considering boundary conditions and entropy control.

Contribution

It provides the first $L^{1}$ existence result for the stationary Boltzmann equation with two components of different molecular masses in a bounded domain.

Findings

Established $L^{1}$ existence under specified boundary conditions.

Derived weak $L^{1}$ compactness from entropy production.

Handled different molecular masses in the two-component gas model.

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 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.