IJPAM: Volume 119, No. 4 (2018)

Title

MATHEMATICAL DESCRIPTION OF THE EQUILIBRIUM
STATE OF SYMMETRIC PARTICLE SYSTEMS

Authors

Halyna M. Hubal
Computer Science and Information Technologies Faculty
Lutsk National Technical University
75 Lvivs'ka str., Lutsk, 43018, UKRAINE

Abstract

One-dimensional symmetric system of particles (hard spheres) is considered in this paper. In equilibrium state of this system, the limit distribution of the configuration Gibbs distribution in the Boltzmann-Grad limit ($d \to 0$, \(n\) is fixed) is uniform (the speed distribution is the Maxwell one and is unchanged).

History

Received: February 22, 2018
Revised: Jule 30, 2018
Published: August 10, 2018

AMS Classification, Key Words

AMS Subject Classification: 35Q82
Key Words and Phrases: BBGKY hierarchy of equations, Maxwell speed distribution, symmetric particle system, equilibrium state

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Bibliography

1
N. N. Bogolyubov, Problems of a dynamical theory instatistical physics, Gosudarstv. Izdat. Tehn.Teor. Lit., Russian Federation(1946) [in Russian].

2
C. Cercignani, V. I. Gerasimenko, D. Ya. Petrina, -particle dynamics and kinetic equations, Kluwer Acad. Publ.,Netherlands (1997), doi: http://dx.doi.org/10.1007/978-94-011-5558-8.

3
G. N. Gubal', On the existence ofweak local in time solutions in the form of a cumulant expansionfor a chain of Bogolyubov's equations of a one-dimensionalsymmetric particle system, Journal of Mathematical Sciences,199 (2014), 654-666, doi: http://dx.doi.org/10.1007/s10958-014-1892-1.

4
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, Siberian Mathematical Journal, 47, No. 1 (2006), 152-168, doi: http://doi.org/10.1007/s11202-006-0015-8.

How to Cite?

DOI: 10.12732/ijpam.v119i4.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 4
Pages: 717 - 726


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