Methods for derivation of the stochastic Boltzmann hierarchy |
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Authors: | D Ya Petrina |
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Institution: | (1) Institute of Mathematics, Ukranian Academy of Sciences, kiev |
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Abstract: | We consider different methods for the derivation of the stochastic Boltzmann hierarchy corresponding to the stochastic dynamics
that is the Boltzmann-Grad limit of the Hamiltonian dynamics of hard spheres. Solutions of the stochastic Boltzmann hierarchy
are the Boltzmann-Grad limit of solutions of the BBGKY hierarchy of hard spheres in the entire phase space. A new concept
of reduced distribution functions corresponding to the stochastic dynamics are introduced. They take into account the contribution
of the hyperplanes of lower dimension where stochastic point particles interact with one another. The solutions of the Boltzmann
equation coincide with one-particle distribution functions of the stochastic Boltzmann hierarchy and are represented by integrals
over the hyperplanes where the stochastic point particles interact with one another. |
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Keywords: | |
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