Abstract
The problem of the existence of solutions of the hierarchy for the sequence of correlation functions is investigated in the direct sum of spaces of summable functions. We prove the existence and uniqueness of solutions, which are represented through a semigroup of bounded strongly continuous operators. The infinitesimal generator of the semigroup coincides on a certain everywhere dense set with the operator on the right-hand side of the hierarchy. For initial data from this set, solutions are strong; for general initial data, they are generalized ones.
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References
D. Ya. Petrina and G. L. Caraffini, “Analog of the Liouville Equation and BBGKY Hierarchy for a System of Hard Spheres with Inelastic Collisions,” Ukr. Mat. Zh., 57, No. 6, 818–839 (2005).
C. Cercignani, V. I. Gerasimenko, and D. Ya. Petrina, Many-Particle Dynamics and Kinetic Equations, Kluwer, Dordrecht (1997).
D. Ya. Petrina, V. I. Gerasimenko, and P. V. Malyshev, Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems, Taylor and Francis, London-New York (2002).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 371–380, March, 2006.
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Petrina, D.Y., Caraffini, G.L. Solutions of the BBGKY hierarchy for a system of hard spheres with inelastic collisions. Ukr Math J 58, 418–429 (2006). https://doi.org/10.1007/s11253-006-0075-8
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DOI: https://doi.org/10.1007/s11253-006-0075-8