Solutions of the BBGKY hierarchy for a system of hard spheres with inelastic collisions

Abstract

The problem of the existence of solutions of the hierarchy for the sequence of correlation functions is investigated in the direct sum of spaces of summable functions. We prove the existence and uniqueness of solutions, which are represented through a semigroup of bounded strongly continuous operators. The infinitesimal generator of the semigroup coincides on a certain everywhere dense set with the operator on the right-hand side of the hierarchy. For initial data from this set, solutions are strong; for general initial data, they are generalized ones.