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Warianty tytułu
Języki publikacji
Abstrakty
We consider a one-dimensional nonsymmetric system of particles interacting via the hard-core potential. For this system, we prove that the BBGKY hierarchy solution in a cumulant representation is an equilibrium in the case of equilibrium initial data.
Czasopismo
Rocznik
Tom
Strony
209--216
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
autor
- Volyn Institute for Postgraduate Pedagogical Education 31 Vynnychenka str., Lutsk 43000, Ukraine
Bibliografia
- [1] N.N. Bogolyubov, Problems of a dynamical theory in statistical physics, Gostekhizdat, Moscow, 1946 [in Russian].
- [2] C. Cercignani, V.I. Gerasimenko, D.Ya. Petrina, Many-particle dynamics and kinetic equations, Kluwer Acad. Publ., Dordrecht, 1997.
- [3] C. Cercignani, R. Illner, M. Pulvirenti, The mathematical theory of dilute gases, Appl. Math. Sci. 106 (1994).
- [4] V.I. Gerasimenko, M.O. Stashenko, Non-equilibrium cluster expansions of non-symmetrical particle systems, Sci. Bulletin of the Volyn State Univ. 4 (2002), 5–13 [in Ukrainian].
- [5] G.N. Gubal’, M.A. Stashenko, Improvement of an estimate of the global existence theorem for solutions of Bogoliubov equations, Teoret. i Mat. Fizika, 145 (3) (2005), 420–424, English transl.: Theoret. and Math. Phys. 145 (3) (2005), 1736–1740.
- [6] R. Illner, M. Pulvirenti, Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum, Commun. Math. Phys. 105 (1986), 189–203.
- [7] R. Illner, M. Pulvirenti, A derivation of the BBGKY hierarchy for hard sphere particle systems, Transp. Theory and Statist. Phys. 16 (7) (1987), 997–1012.
- [8] D.Ya. Petrina, Mathematical description of the evolution of infinite systems of classical statistical physics. I. Locally perturbed one-dimensional systems, Teoret. i Mat. Fizika 38 (2) (1979), 230–250 [in Russian].
- [9] D.Ya. Petrina, V.I. Gerasimenko, Mathematical description of the evolution of the state of infinite systems of classical statistical mechanics, Uspekhi Mat. Nauk 38 (5) (1983), 3–58 [in Russian].
- [10] D.Ya. Petrina, V.I. Gerasimenko, Evolution of states of infinite systems in classical statistical mechanics, Sov. Sci. Rev. Ser. C: Math. Phys. 5 (1985), 1–52.
- [11] D.Ya. Petrina, V.I. Gerasimenko, Mathematical problems of statistical mechanics of a system of elastic balls, Uspekhi Mat. Nauk 45 (3) (1990), 135–182 [in Russian].
- [12] D.Ya. Petrina, V.I. Gerasimenko, P.V. Malyshev, Mathematical foundations of classical statistical mechanics. Continuous systems, 2nd ed. Taylor and Francis, London, 2002.
- [13] M.O. Stashenko, H.M. Hubal, A local existence theorem of the solution of the Cauchy problem for BBGKY chain of equations represented in cumulant expansions in the space E ξ, Opuscula Mathematica 24 (1) (2004), 161–168.
- [14] M.A. Stashenko, G.N. Gubal’, Existence theorems for the initial value problem for the Bogolyubov chain of equations in the space of sequences of bounded functions, Sib. Mat. Zhurn. 47 (1) (2006), 188–205, English transl.: Siberian Math. J. 47 (1) (2006), 152–168.
- [15] V.I. Gerasimenko, Thermodynamic limit in classical non-equilibrium system. The case of the nearest particle interaction, Prepr. Acad. Sciences Ukr. Inst. Theoretical Phys., 58P (1980) [in Russian].
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0001-0012