Incollection,
On regularized solution of BBGKY hierarchy \\ for infinitely particle systems
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
We construct a solution to the initial-value problem of the BBGKY
hierarchy for infinitely particle one-dimensional systems. The
solution represents as an expansion in terms of particle clusters
whose evolution is described by the corresponding order cumulant
(semi-invariant) of the evolution operators of finitely many
particle systems. We establish the local in time existence theorem
of a weak solution for initial data from the space of sequences of
bounded functions. In this space the stated cumulant nature of the
solution expansion guarantee the compensation of divergent integrals
over the configuration variables in every term.
Using the cumulant representation of a solution to the
initial-value problem of the dual BBGKY hierarchy we investigate
the existence of functionals for average values of observables of
considered system.
