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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 3, Pages 59–73
DOI: https://doi.org/10.33048/sibjim.2018.22.306 (Mi sjim1054) 		 
On one system of ordinary differential equations of large dimension and a delay equation

G. V. Demidenkoab, I. A. Uvarovaba, Yu. A. Khazovac

a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, 630090 Novosibirsk
b Novosibirsk State University, ul. Pirogova 1, 630090 Novosibirsk
c V.I. Vernadsky Crimean Federal University, pr. Akad. Vernadskogo 4, 295007 Simferopol'
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DOI: https://doi.org/10.33048/sibjim.2018.22.306
Abstract: We consider some system of ordinary differential equations modeling a multistage synthesis of a substance. We prove the global limit theorems that establish connections between the solutions to a system of ordinary differential equations of large dimension and the solutions to a delay equation. The obtained results enable us to find the approximate solutions to the systems under consideration of an arbitrarily high dimension on the whole half-axis. Some approximation estimates are established.
Keywords: system of ordinary differential equations of high dimension, delay equation, global limit theorem, approximation estimate.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10086_мк
Ministry of Education and Science of the Russian Federation
Received: 08.05.2019
Revised: 08.05.2019
Accepted: 13.06.2019
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 3, Pages 447–459
DOI: https://doi.org/10.1134/S1990478919030062
Bibliographic databases:
Document Type: Article
UDC: 517.925.5:517.929
Language: Russian
Citation: G. V. Demidenko, I. A. Uvarova, Yu. A. Khazova, “On one system of ordinary differential equations of large dimension and a delay equation”, Sib. Zh. Ind. Mat., 22:3 (2019), 59–73; J. Appl. Industr. Math., 13:3 (2019), 447–459
Citation in format AMSBIB
\Bibitem{DemUvaKha19}
\by G.~V.~Demidenko, I.~A.~Uvarova, Yu.~A.~Khazova
\paper On one system of ordinary differential equations of large dimension and a delay equation
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 3
\pages 59--73
\mathnet{http://mi.mathnet.ru/sjim1054}
\crossref{https://doi.org/10.33048/sibjim.2018.22.306
}
\elib{https://elibrary.ru/item.asp?id=41633016}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 3
\pages 447--459
\crossref{https://doi.org/10.1134/S1990478919030062}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071421824}
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