Abstract
Evolution equations for marginal generalized microscopic phase densities are introduced. The evolution equations for average values of microscopic phase densities are derived and a solution of the initial-value problem for the hydrodynamic type hierarchy obtained is constructed.
[1] Yu.L. Klimontovich, V.P. Silin, Zhurn. Exp. Teor. Fiz. 23, 151 (1952) Search in Google Scholar
[2] Yu.L. Klimontovich, Statistical Physics (Harwood Acad. Publ., London, 1986) Search in Google Scholar
[3] R. Balescu, Aspects of Anomalous Transport in Plasmas (Institute of Physics, Bristol, 2005) http://dx.doi.org/10.1201/978142003468410.1201/9781420034684Search in Google Scholar
[4] Yu.L. Klimontovich, H. Wilhelmsson, I.P. Yakimenko, A.G. Zagorodny, Statistical Theory of Plasma-Molecular Systems (Moscow State Univ. Press, Moscow, 1990) Search in Google Scholar
[5] A.G. Sitenko, A.G. Zagorodny, Ukr. J. Phys. 45, 446 (2000) Search in Google Scholar
[6] A. Zagorodny, J. Weiland, Phys. Plasmas 16, 052308 (2009) http://dx.doi.org/10.1063/1.312530610.1063/1.3125306Search in Google Scholar
[7] N.N. Bogolyubov, Problems of Dynamic Theory in Statistical Physics (FITTL, Moscow, 1946) Search in Google Scholar
[8] C. Cercignani, V.I. Gerasimenko, D.Ya. Petrina, Many-Particle Dynamics and Kinetic Equations (Kluwer, Amsterdam, 1997) http://dx.doi.org/10.1007/978-94-011-5558-810.1007/978-94-011-5558-8Search in Google Scholar
[9] G. Borgioli, V.I. Gerasimenko, Riv. Mat. Univ. Parma 4, 251 (2001) Search in Google Scholar
[10] D.Ya. Petrina, V.I. Gerasimenko, Uspekhi Mat. Nauk 45, 135 (1990) Search in Google Scholar
[11] V.I. Gerasimenko, T.V. Ryabukha, M.O. Stashenko, J. Phys. A: Math. Gen. 37, 9861 (2004) http://dx.doi.org/10.1088/0305-4470/37/42/00210.1088/0305-4470/37/42/002Search in Google Scholar
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