This paper proposes a semicontinuous model of the Boltzmann equation to describe the behavior of a mixture of P gases. The semicontinuous Boltzmann equation is a model in which gas particles can move in the plane in all possible directions, but with a finite number of velocity moduli. The model consists of a system of integro-differential equations with one-fold integrals over a suitable angular variable. Thermodynamic equilibrium is studied in details showing that the Maxwellian equilibrium states are uniquely defined in terms of the masses of the components of the mixtures and of the overall momentum and energy.
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Luigi Preziosi (1993) studied this question.