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pro vyhledávání: '"Gapyak, I. V."'
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
In: Modern Problems of Mathematics and its Applications. III. (Eds. V.I. Gerasimenko et al.), Kyiv: IM, 2023, 729-804. ISSN: 1815-2910. The book is dedicated to the 160th anniversary of the birth of academician D. O. Grave
The review presents rigorous results of the theory of fundamental equations of evolution of many-particle systems with collisions and also considers their connection with nonlinear kinetic equations describing the collective behavior of particles in
Externí odkaz:
http://arxiv.org/abs/2308.04143
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
AIP Advances, 14 125006 (2024)
The article deals with the challenge of the construction of solutions to hierarchies of fundamental evolution equations for many colliding particles. The method of cluster expansions of the groups of operators of the Liouville equations for observabl
Externí odkaz:
http://arxiv.org/abs/2307.02121
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
J Stat Phys 189, 2 (2022)
The paper develops an approach to the description of the evolution of correlations for many hard spheres based on a hierarchy of evolution equations for the cumulants of the probability distribution function governed by the Liouville equation. It is
Externí odkaz:
http://arxiv.org/abs/2111.13940
Autor:
Gerasimenko, V. I., Gapyak, I. V.
The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an approach to the description of the evolution based on the dynamics of cor
Externí odkaz:
http://arxiv.org/abs/2012.03001
Autor:
Gerasimenko, V. I., Gapyak, I. V.
Publikováno v:
Reviews in Mathematical Physics, 33 (2021) 2130001 (32 pages)
The article discusses some of the latest advances in the mathematical understanding of the nature of kinetic equations that describe the collective behavior of many-particle systems with collisional dynamics.
Comment: 30 pages. arXiv admin note:
Comment: 30 pages. arXiv admin note:
Externí odkaz:
http://arxiv.org/abs/2001.06786
Autor:
Gapyak, I. V., Gerasimenko, V. I.
Publikováno v:
Math. Bulletin Sh. Sci. Soc. 9 (2012) 23-43
The rigorous approach to the description of the kinetic evolution of a many-particle system composed of a trace hard sphere and an environment of finitely many hard spheres is developed. We prove that the evolution of states of a trace hard sphere in
Externí odkaz:
http://arxiv.org/abs/1208.1647
Autor:
Gapyak, I. V., Gerasimenko, V. I.
Publikováno v:
Kinet. Relat. Models 5 (3) (2012) 459-484
We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear kinetic Ensko
Externí odkaz:
http://arxiv.org/abs/1107.5572
Autor:
Gerasimenko, V. I., Gapyak, I. V.
The communication deals with the problem of a rigorous description of the evolution of the observables of many colliding particles. The method of cluster expansions of the groups of operators of the Liouville equations is used to establish the genera
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::541dbc9b42bc39611a68abe0f9b95015
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