Abstract
The kinetic equation proposed in [1,2] for describing the behavior of a system of particles in a gas flow differs from the usual Boltzmann equation with respect to the additional terms that take into account random variations of the particle velocity under the influence of the flow. As shown in [2], the collision operator and the Brownian-type operator in the starting kinetic equation describe essentially different simultaneous physical processes of change of state of the particle system: equalization of the mean kinetic energy of the particles and change of energy due to the action of the viscous forces associated with the suspending flow. Therefore the method of solving the kinetic equation used in [2], a direct generalization of the Chapman-Enskog method of solving the kinetic equation it is necessary to investigate method of solving the kinetic equation it is necessar y to investigate the relaxation processes in the system. Moreover, the relaxation of systems of the fluidized-bed type to the continuum state is also of independent interest in connection with the analysis of fast processes in the system, i.e., processes with a characteristic duration of the order of the mean free time.
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