Construction of generalized normal solutions of kinetic equations for a mixture of gases

A method of constructing generalized normal solutions of kinetic equations by means of initial conditions [1] is applied to a multicomponent mixture of gases. Integral equations are obtained for the distribution functions, in which allowance is made for initial conditions that ensure the selection of normal solutions. For the solving of these integral equations a regular method of successive approximations is constructed, this corresponding to an expansion of the distribution functions and the fluxes in the first order in the small gradients of the hydrodynamic variables. The fluxes are related integrally to the thermodynamic foYces, which correspond to allowance for “memory” effects.