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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 1, Pages 58–68
(Mi smj848)
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This article is cited in 19 scientific papers (total in 19 papers)
On one class of systems of differential equations and on retarded equations
G. V. Demidenkoa, V. A. Likhoshvaib, T. V. Kotovac, Yu. E. Khropovac a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Institute of cytology and genetics
Siberian Branch of the Russian Academy of Sciences
c Novosibirsk State University, Mechanics and Mathematics Department
Abstract:
We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis.
Keywords:
retarded differential equations, weak solution.
Received: 21.10.2005
Citation:
G. V. Demidenko, V. A. Likhoshvai, T. V. Kotova, Yu. E. Khropova, “On one class of systems of differential equations and on retarded equations”, Sibirsk. Mat. Zh., 47:1 (2006), 58–68; Siberian Math. J., 47:1 (2006), 45–54
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https://www.mathnet.ru/eng/smj848 https://www.mathnet.ru/eng/smj/v47/i1/p58
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