Gorev V. Reduced description of non-equilibrium systems with account for relaxation processes.

The object of research is a one-component gas and a completely ionized two-component plasma. The aim of research is a generalization of the Chapman-Enskog method to the case of the presence of relaxation processes in a system. The term "relaxation process" is understood in a narrow sense as a process which can take place in the spatially uniform case. The methods of research are the Bogolyubov reduced description method, the Bogolyubov idea of functional hypothesis, the Chapman-Enskog method and the method of Sonine polynomial expansion. The theoretical and practical results are that a general theory of relaxation processes in the vicinity of hydrodynamic states (generalized Chapman-Enskog method) is developed on the basis of the kinetic equation. The relaxation processes are considered at their end. The Grad problem is investigated on the basis of this method. Corrections to the Grad results are obtained in the two-polynomial approximation. Relaxation in a spatially uniform plasma is investigated. Corrections to the results of the local equilibrium assumption for the component distribution functions and temperature and velocity relaxation rates are obtained. The effect of relaxation processes on the hydrodynamics and modes of plasma are investigated with consistent account for the dynamics of the ion component. The field of use is that the developed generalized Chapman-Enskog method can be used for the investigation of the effect of relaxation processes on hydrodynamic phenomena in gases, liquids, plasma, solids. It allows one to account for new relaxation degrees of freedom of the system and go beyond the local equilibrium assumption.