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TMF, 1972, Volume 13, Number 3, Pages 406–420 (Mi tmf3277)  

This article is cited in 11 scientific papers (total in 11 papers)

Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy

D. N. Zubarev, M. Yu. Novikov


Abstract: A generalized formulation of the boundary condition of correlation weakening for the Liouville equation is presented; it is based on the introduction of an infinitesimally small source that breaks the symmetry of this equation under time reversal. This leads to the BBGKY hierarchy of equations with boundary conditions for all the reduced distribution functions except the first or except the first and second. It is shown that, irrespective of the existence of a small parameter, one can obtain closed kinetic equations for the single-particle or the twoparticle distribution function.

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English version:
Theoretical and Mathematical Physics, 1972, 13:3, 1229–1238

Received: 15.06.1972

Citation: D. N. Zubarev, M. Yu. Novikov, “Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy”, TMF, 13:3 (1972), 406–420; Theoret. and Math. Phys., 13:3 (1972), 1229–1238

Citation in format AMSBIB
\Bibitem{ZubNov72}
\by D.~N.~Zubarev, M.~Yu.~Novikov
\paper Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy
\jour TMF
\yr 1972
\vol 13
\issue 3
\pages 406--420
\mathnet{http://mi.mathnet.ru/tmf3277}
\transl
\jour Theoret. and Math. Phys.
\yr 1972
\vol 13
\issue 3
\pages 1229--1238
\crossref{https://doi.org/10.1007/BF01036148}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Yu. Novikov, “Master equation and Bogolyubov's method of functional expansions”, Theoret. and Math. Phys., 16:3 (1973), 920–928  mathnet  crossref  mathscinet
    2. R. M. Yul'met'yev, “Investigation of invariants of a many-particle system by the method of projection operators”, Theoret. and Math. Phys., 20:3 (1974), 914–922  mathnet  crossref  mathscinet
    3. D. N. Zubarev, M. Yu. Novikov, “Diagram method of constructing solutions of Bogolyubov's chain of equations”, Theoret. and Math. Phys., 18:1 (1974), 55–62  mathnet  crossref  mathscinet  zmath
    4. L. Ts. Adzhemyan, F. M. Kuni, T. Yu. Novozhilova, “Nonlinear generalization of Mori's method of projection operators”, Theoret. and Math. Phys., 18:3 (1974), 274–280  mathnet  crossref  mathscinet  zmath
    5. A. V. Prozorkevich, S. A. Smolyanskii, “Derivation of relativistic transport equations of a plasma in a strong electromagnetic field”, Theoret. and Math. Phys., 23:3 (1975), 608–614  mathnet  crossref
    6. R. M. Yul'met'yev, “Bogolyubov's abridged description of equilibrium systems and derivation of an equation for the radial distribution function in a liquid”, Theoret. and Math. Phys., 25:2 (1975), 1100–1108  mathnet  crossref  mathscinet
    7. D. N. Zubarev, A. M. Khazanov, “Generalized Fokker–Planck equation and construction of projection operators for different methods of reduced description of nonequilibrium states”, Theoret. and Math. Phys., 34:1 (1978), 43–50  mathnet  crossref  mathscinet
    8. D. N. Zubarev, V. G. Morozov, “Formulation of boundary conditions for the BBGKY hierarchy with allowance for local conservation laws”, Theoret. and Math. Phys., 60:2 (1984), 814–820  mathnet  crossref  mathscinet  isi
    9. E. F. Popov, “Statistical description of a system of charged particles”, Theoret. and Math. Phys., 76:3 (1988), 981–989  mathnet  crossref  mathscinet  isi
    10. D. N. Zubarev, V. G. Morozov, I. P. Omelyan, M. V. Tokarchuk, “Kinetic equations for dense gases and liquids”, Theoret. and Math. Phys., 87:1 (1991), 412–424  mathnet  crossref  mathscinet  zmath  isi
    11. Tarasov, VE, “Fokker-Planck equation for fractional systems”, International Journal of Modern Physics B, 21:6 (2007), 955  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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