On the Bogolubov’s chain of kinetic equations, the invariant subspaces and the corresponding Dirac type reduction

Yarema A Prykarpatsky, Radoslaw Kycia and Anatolij K Prykarpatski*

We study a special class of dynamical systems of Boltzmann-Bogolubov and Boltzmann-Vlasov type on infinite 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 infinite 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 modified Boltzmann-Bogolubov kinetic equations on a finite set of multiparticle distribution functions. 

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Published on: Oct 14, 2021 Pages: 74-83

Full Text PDF Full Text HTML DOI: 10.17352/amp.000026
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