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On the property of the BBGKY hierarchy solution in a cumulant representation

Stashenko M. O., Hubal H. M.

Opuscula Mathematica

2009

Vol. 29, no. 2

209-216

We consider a one-dimensional nonsymmetric system of particles interacting via the hard-core potential. For this system, we prove that the BBGKY hierarchy solution in a cumulant representation is an equilibrium in the case of equilibrium initial data.

A local existence theorem of the solution of the Cauchy problem for BBGKY chain of equations represented in cumulant expansions in the space Eξ

Stashenko M.O., Hubal H.M.

Opuscula Mathematica

2004

Vol. 24, no. 1

161-168

It is proved convergence of solution in cumulant expansions of the initial value problem for BBGKY chain of equations of non-symmetrical one-dimensional system of particles which interact via a short-range potential in the space Eξ of the sequences of continuous bounded functions.