Abstract:
A generalized solution is constructed for the hierarchy of coupled
diffusion equations for the sequence of correlation functions of
interacting particles diffusing in a fluid. At the initial time,
this solution is identical to Gibbs correlation functions. The
solution is obtained in the form of a series in powers of the
activity, and the series converges uniformly over a finite time
interval.
Citation:
V. I. Skripnik, “Generalized solutions of Gibbs type for the Bogolyubov–Strel'tsova diffusion hierarchy”, TMF, 58:3 (1984), 398–420; Theoret. and Math. Phys., 58:3 (1984), 260–275
\Bibitem{Skr84}
\by V.~I.~Skripnik
\paper Generalized solutions of Gibbs type for the Bogolyubov--Strel'tsova diffusion hierarchy
\jour TMF
\yr 1984
\vol 58
\issue 3
\pages 398--420
\mathnet{http://mi.mathnet.ru/tmf4672}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=752075}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 58
\issue 3
\pages 260--275
\crossref{https://doi.org/10.1007/BF01018049}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984TJ86800009}
Linking options:
https://www.mathnet.ru/eng/tmf4672
https://www.mathnet.ru/eng/tmf/v58/i3/p398
This publication is cited in the following 5 articles:
A. I. Pilyavskii, A. L. Rebenko, V. I. Skripnik, “Generalized solutions of the Bogolyubov diffusion hierarchy in the thermodynamic limit. Cluster expansions”, Theoret. and Math. Phys., 93:1 (1992), 1160–1172
V. I. Skripnik, “Evolution operator of the Bogolyubov gradient diffusion hierarchy in the mean field limit”, Theoret. and Math. Phys., 79:1 (1989), 431–436
R. L. Dobrushin, Ya. G. Sinai, Yu. M. Sukhov, Encyclopaedia of Mathematical Sciences, 2, Dynamical Systems II, 1989, 208
V. I. Skripnik, “Mean field limit in a generalized Gibbs system and the equivalent nonequilibrium system of interacting Brownian particles”, Theoret. and Math. Phys., 76:1 (1988), 734–746
V. I. Skripnik, “Smoluchowski diffusion in an infinite system at low density: Local time evolution”, Theoret. and Math. Phys., 69:1 (1986), 1047–1056
Citation in format AMSBIB
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