The stationary Boltzmann equation for a two-component gas in the slab with different molecular masses. (English) Zbl 1337.35108

Brull, Stéphane

Adv. Differ. Equ. 15, No. 11-12, 1103-1124 (2010).

Summary: 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.

MSC:

35Q20	Boltzmann equations
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35D30	Weak solutions to PDEs
45K05	Integro-partial differential equations
82C40	Kinetic theory of gases in time-dependent statistical mechanics