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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 12, Pages 2050–2058
DOI: https://doi.org/10.31857/S0044466921120188 (Mi zvmmf11330) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Partial Differential Equations

Asymptotics of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables

A. V. Zaborskiya, A. V. Nesterovb, D. Yu. Nechaevb

a "RADICO" Scientific Production Company, 249035, Obninsk, Kaluga oblast, Russia
b Plekhanov Russian University of Economic, 117997, Moscow, Russia
Citations (4)
DOI: https://doi.org/10.31857/S0044466921120188
Abstract: A formal asymptotic expansion of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables with weak nonlinearity is constructed. Under certain conditions imposed on the data of the problem, the asymptotic expansion is constructed in the form of series in powers of a small parameter with coefficients depending on various stretched variables. Problems for determining all terms of the asymptotic expansion are obtained. Specifically, the leading term is determined as the solution of the Cauchy problem for a parabolic equation. The remainder is estimated with respect to the residual.
Key words: partial differential operator equations, Cauchy problem, small nonlinearity, singular perturbations, asymptotic expansions, parabolic equations.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation FSSW-2020-0008
This research was supported by the Ministry of Science and Higher Education of the Russian Federation within the state assignment “Development of methodology and program platform for construction of digital twins, data mining, and forecasting of complex economic systems”, project no. FSSW-2020-0008.
Received: 16.02.2021
Revised: 28.04.2021
Accepted: 04.08.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 12, Pages 2015–2023
DOI: https://doi.org/10.1134/S0965542521120174
Bibliographic databases:
Document Type: Article
UDC: 517.955
Language: Russian
Citation: A. V. Zaborskiy, A. V. Nesterov, D. Yu. Nechaev, “Asymptotics of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 2050–2058; Comput. Math. Math. Phys., 61:12 (2021), 2015–2023
Citation in format AMSBIB
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\paper Asymptotics of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2021
\vol 61
\issue 12
\pages 2050--2058
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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