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 CMFD, 2011, Volume 42, Pages 82–94 (Mi cmfd192)

On the existence of weak local in time solutions in the form of a cumulant expansion for a chain of Bogolyubov's equations of a one-dimensional symmetric particle system

G. N. Gubal'

Lutsk National Technical University, Ukraine, 43018, Lutsk, L'vovskaya, 75

Abstract: We consider a Cauchy problem for a chain of Bogolyubov equations of an infinite one-dimensional symmetric particle system, where the particles interact with each other by a finite-range pair potential with a hard core. We consider it in the space of sequences of bounded measurable functions. Based on the proposed method of a joint interval for estimates of the volume of the interaction domain and on the derived estimate itself we find a representation of a weak local with respect to time solution in the form of a cumulant expansion. We prove that the considered weak local with respect to time solution is an equilibrium solution if the initial data are equilibrium distribution functions.

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English version:
Journal of Mathematical Sciences, 2014, 199:6, 654–666

Bibliographic databases:

UDC: 517.9+531.19

Citation: G. N. Gubal', “On the existence of weak local in time solutions in the form of a cumulant expansion for a chain of Bogolyubov's equations of a one-dimensional symmetric particle system”, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), CMFD, 42, PFUR, M., 2011, 82–94; Journal of Mathematical Sciences, 199:6 (2014), 654–666

Citation in format AMSBIB
\Bibitem{Gub11} \by G.~N.~Gubal' \paper On the existence of weak local in time solutions in the form of a~cumulant expansion for a~chain of Bogolyubov's equations of a~one-dimensional symmetric particle system \inbook Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3--7, 2009) \serial CMFD \yr 2011 \vol 42 \pages 82--94 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd192} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013830} \transl \jour Journal of Mathematical Sciences \yr 2014 \vol 199 \issue 6 \pages 654--666 \crossref{https://doi.org/10.1007/s10958-014-1892-1} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902831845}