Gapyak I. Kinetic equations of hard sphere systems and properties of their solutions

The thesis is devoted to the problem of the justification of the Enskog kinetic equation and the Fokker - Planck kinetic equation for systems particles interacting via the singular interaction potential. In this thesis a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres is developed. On basis of introduced kinetic cluster expansions of the cumulants of groups of operators of finitely many hard spheres generalization of the Enskog kinetic equation is rigorously derived. It is proved that the evolution of states of a trace hard sphere in the Enskog gas can be described within the framework of the marginal distribution function governed by the generalized Fokker- Planck kinetic equation and an infinite sequence of the explicitly defined marginal functionals. In the space of integrable functions the existence theorems forthe Cauchy problem of the generalized Enskog kinetic equation and the Cauchy problem of the generalized Fokker - Planck kinetic equation for hard sphere systems are proved and their properties are investigated.