Methods for derivation of the stochastic Boltzmann hierarchy
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 t...
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| Date: | 2000 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2000
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157605 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Methods for derivation of the stochastic Boltzmann hierarchy / D.Ya. Petrina // Український математичний журнал. — 2000. — Т. 52, № 4. — С. 474–491. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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