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
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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Journal of Mathematical Sciences, 2014, 199:6, 654–666
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
\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)
\jour Journal of Mathematical Sciences
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