On the Bogolubov’s chain of kinetic equations, the invariant subspaces and the corresponding Dirac type reduction
Authors:
- Yarema A Prykarpatsky,
- Radosław Kycia,
- Anatlolij K Prykarpatski
Abstract
We study a special class of dynamical systems of Boltzmann-Bogolubov and Boltzmann-Vlasov type on infi nite dimensional functional manifolds modeling kinetic processes in manyparticle media. Based on geometric properties of the manyparticle phase space we succeded in dual analysing of the infi nite Bogolubov hierarchy of manyparticle distribution functions and their Hamiltonian structure. Moreover, we proposed a new approach to invariant reducing the Bogolubov hierarchy on a suitably chosen correlation function constraint and deducing the related modifi ed Boltzmann-Bogolubov kinetic equations on a fi nite set of multiparticle distribution functions.
- Record ID
- CUT6fa8a28818824ff49687be59bc90fa9b
- Publication categories
- ;
- Author
- Journal series
- Annals of Mathematics and Physics, ISSN 2689-7636
- Issue year
- 2021
- Vol
- 4
- No
- 1
- Pages
- 074-083
- Other elements of collation
- Bibliografia (na s.) - 082-083; Bibliografia (liczba pozycji) - 43; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 4, Iss. 1
- Keywords in English
- multi-particle distribution functions, Boltzmann kinetic equations, Bogolubov kinetik equations chain, Wigner transformation, functional equations, canonical poisson bracket, Lie-poisson brackets, Dirac reduction theory, invariant functional submanifolds
- DOI
- DOI:10.17352/amp.000026 Opening in a new tab
- URL
- https://www.peertechzpublications.com/articles/AMP-4-126.php Opening in a new tab
- Related project
- Teoria równań i nierówności różniczkowych, układy dynamiczne na rozmaitościach, wybrane działy: analizy matematycznej topologii algebry i geometrii oraz probabilistyki teorii grafów i liczb. . Project leader at PK: , ,
Działalność statutowa - Language
- eng (en) English
- License
- Score (nominal)
- 5
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT6fa8a28818824ff49687be59bc90fa9b/
- URN
urn:pkr-prod:CUT6fa8a28818824ff49687be59bc90fa9b
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