Fokker-Planck equation with initial correlations in kinetic collision theory

Gapiak Igor Vasyliovych; Gerasimenko Viktor Ivanovich

Gapiak Igor Vasyliovych ¹ , Gerasimenko Viktor Ivanovich ²

¹ Department of Computer Graphics and Visualization, Taras Shevchenko National University of Kyiv, Kyiv, 03127, Ukraine

² Department of nonlinear analysis, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, 01001, Ukraine

Keywords: Fokker-Planck equation, initial correlations in kinetic collision theory

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Abstract

The problem of the description of the kinetic evolution of a multi-particle system composed of a tracer hard sphere and an environment of finitely many hard spheres in the presence of initial correlations is considered. We prove that the evolution of a state of a tracer hard sphere is described within the framework of the generalized Fokker - Planck kinetic equation with initial correlations. The processes of the propagation of initial correlations and the creation of correlations in a system described by means of an innite sequence of the explicitly defined functionals with respect to a solution of the constructed kinetic equation are described.

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ACS Style: Gapiak, I.V.; Gerasimenko, V.I. Fokker-Planck equation with initial correlations in kinetic collision theory. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Gapiak IV, Gerasimenko VI. Fokker-Planck equation with initial correlations in kinetic collision theory. Bukovinian Mathematical Journal. 2016; 3(3-4).
Chicago/Turabian Style: Igor Vasyliovych Gapiak, Viktor Ivanovich Gerasimenko. 2016. "Fokker-Planck equation with initial correlations in kinetic collision theory". Bukovinian Mathematical Journal. 3 no. 3-4.

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