On nonlinear theory dynamics of dilute gas

In framework of BGK (Bhatnagar, Gross and Kruck) model the boundary-value problem for nonlinear integro-differential Boltzmann equation is considered. By means of corresponding transformations, the problem is reduced to «weak» connected quazilinear system of integral equations. Such normal form of Boltzmann equation allow us to analyse statement of boundary-value problem and to suggest effective methods for it solution. As example, the results for two classic problems of kinetic theory of gases are applied.