Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 053, 8 pages      cond-mat/0605364      http://dx.doi.org/10.3842/SIGMA.2006.053

On Regularized Solution for BBGKY Hierarchy of One-Dimensional Infinite System

Tatiana V. Ryabukha
Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine

Received October 31, 2005, in final form April 26, 2006; Published online May 14, 2006

Abstract
We construct a regularized cumulant (semi-invariant) representation of a solution of the initial value problem for the BBGKY hierarchy for a one-dimensional infinite system of hard spheres interacting via a short-range potential. An existence theorem is proved for the initial data from the space of sequences of bounded functions.

Key words: BBGKY hierarchy; cumulant; regularized solution.

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