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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, Issue 1(30), Pages 270–278 (Mi vsgtu1216)  

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Mechanics and Classical Field Theory

On a rigorous definition of microscopic solutions of the Boltzmann–Enskog equation

A. S. Trushechkin

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, 119991, Russia

Abstract: N. N. Bogolyubov discovered microscopic solutions of the Boltzmann–Enskog equation in kinetic theory of hard spheres. These solutions have the form of sums of the delta-functions and correspond to the exact microscopic dynamics. However, this was done at the “physical level” of rigour. In particular, Bogolyubov did not discuss the products of generalized functions in the collision integral. Here we give a rigorous sense to microscopic solutions by use of regularization. Also, starting from the Vlasov equaton, we obtain new kinetic equations for a hard sphere gas.

Keywords: kinetic equations, Boltzmann–Enskog equation, Vlasov equation, microscopic solutions, generalized functions

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-37273
Ministry of Education and Science of the Russian Federation 2928.2012.1
8215


DOI: https://doi.org/10.14498/vsgtu1216

Full text: PDF file (188 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.958
MSC: Primary 82C40; Secondary 82C70, 35Q20, 35Q83
Original article submitted 19/XI/2012
revision submitted – 27/I/2013

Citation: A. S. Trushechkin, “On a rigorous definition of microscopic solutions of the Boltzmann–Enskog equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 270–278

Citation in format AMSBIB
\Bibitem{Tru13}
\by A.~S.~Trushechkin
\paper On a rigorous definition of microscopic solutions of the Boltzmann--Enskog equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 270--278
\mathnet{http://mi.mathnet.ru/vsgtu1216}
\crossref{https://doi.org/10.14498/vsgtu1216}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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