# American Institute of Mathematical Sciences

March  2013, 6(1): 137-157. doi: 10.3934/krm.2013.6.137

## Diffusion asymptotics of a kinetic model for gaseous mixtures

 1 UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005 2 MAP5, CNRS UMR 8145, Université Paris Descartes, Sorbonne Paris Cité, 45 Rue des Saints Pères, F-75006 Paris, France 3 CMLA, ENS Cachan, PRES UniverSud Paris, 61 Avenue du Président Wilson, F-94235 Cachan Cedex, France 4 Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1 - 27100 Pavia

Received  July 2012 Revised  October 2012 Published  December 2012

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 Grad cannot be applied, and we propose a new method to treat the terms involving particles with different masses.
Citation: Laurent Boudin, Bérénice Grec, Milana Pavić, Francesco Salvarani. Diffusion asymptotics of a kinetic model for gaseous mixtures. Kinetic & Related Models, 2013, 6 (1) : 137-157. doi: 10.3934/krm.2013.6.137
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