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This article is cited in 1 scientific paper (total in 1 paper)
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
(published under the terms of the Creative Commons Attribution 4.0 International License)
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.
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
Linking options:
https://www.mathnet.ru/eng/vsgtu1216 https://www.mathnet.ru/eng/vsgtu/v130/p270
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