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Tr. Mat. Inst. Steklova, 2014, Volume 285, Pages 264–287 (Mi tm3549)  

This article is cited in 2 scientific papers (total in 2 papers)

Microscopic solutions of kinetic equations and the irreversibility problem

A. S. Trushechkinab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Engineering Physics Institute "MEPhI", Moscow, Russia

Abstract: As established by N. N. Bogolyubov, the Boltzmann–Enskog kinetic equation admits the so-called microscopic solutions. These solutions are generalized functions (have the form of sums of delta functions); they correspond to the trajectories of a system of a finite number of balls. However, the existence of these solutions has been established at the “physical” level of rigor. In the present paper, these solutions are assigned a rigorous meaning. It is shown that some other kinetic equations (the Enskog and Vlasov–Enskog equations) also have microscopic solutions. In this sense, one can speak of consistency of these solutions with microscopic dynamics. In addition, new kinetic equations for a gas of elastic balls are obtained through the analysis of a special limit case of the Vlasov equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-37273-mol_a
Ministry of Education and Science of the Russian Federation NSh-864.2014.1
8215
This work was supported in part by the Russian Foundation for Basic Research (project no. 12-01-37273-mol_a), by a grant of the President of the Russian Federation (project no. NSh-864.2014.1), and by the Ministry of Education and Science of the Russian Federation (project no. 8215).


DOI: https://doi.org/10.1134/S0371968514020186

Full text: PDF file (298 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 285, 251–274

Bibliographic databases:

Document Type: Article
UDC: 517.958+517.968.7
Received in January 2014

Citation: A. S. Trushechkin, “Microscopic solutions of kinetic equations and the irreversibility problem”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Tr. Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 264–287; Proc. Steklov Inst. Math., 285 (2014), 251–274

Citation in format AMSBIB
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\paper Microscopic solutions of kinetic equations and the irreversibility problem
\inbook Selected topics of mathematical physics and analysis
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 285
\pages 264--287
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968514020186}
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  • https://doi.org/10.1134/S0371968514020186
  • http://mi.mathnet.ru/eng/tm/v285/p264

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Trushechkin A., “Microscopic and Soliton-Like Solutions of the Boltzmann Enskog and Generalized Enskog Equations For Elastic and Inelastic Hard Spheres”, Kinet. Relat. Mod., 7:4 (2014), 755–778  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. Pulvirenti, S. Simonella, A. Trushechkin, “Microscopic solutions of the Boltzmann-Enskog equation in the series representation”, Kinet. Relat. Mod., 11:4, SI (2018), 911–931  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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