Stationary solutions to the relativistic BGK model for gas mixtures in a slab

Abstract

In a recent paper [16], the authors proposed a BGK model for relativistic gas mixtures based on the Marle-type approximation, which satisfies the fundamental kinetic properties: non-negativity of distribution functions, conservation laws, H-theorem, and indifferentiability principle. In this paper, we are concerned with the stationary problems to the relativistic BGK model for gas mixtures in slab geometry. We establish the existence of a unique mild solution with the fixed inflow boundary data when the collision frequencies for each species are sufficiently small.