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Diffusion asymptotics of a kinetic model for gaseous mixtures. (English) Zbl 1260.35100

Summary: In this work, we consider the non-reactive fully elastic Boltzmann equations for mixtures in the diffusive scaling. We mainly use a Hilbert expansion of the distribution functions. After briefly recalling the H-theorem, the lower-order non trivial equality obtained from the Boltzmann equations leads to a linear functional equation in the velocity variable. This equation is solved thanks to the Fredholm alternative. Since we consider multicomponent mixtures, the classical techniques introduced by H. Grad [Phys. Fluids 6, 147–181 (1963; Zbl 0115.45006)] cannot be applied, and we propose a new method to treat the terms involving particles with different masses.

MSC:

35Q20 Boltzmann equations
45B05 Fredholm integral equations
35Q35 PDEs in connection with fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics

Citations:

Zbl 0115.45006
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