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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 3, Pages 526–533
DOI: https://doi.org/10.31857/S0044466924030128 (Mi zvmmf11723) 		 
Mathematical physics

On asymptotics of the solution to the Cauchy problem for a singularly perturbed operator-differential transport equation with weak diffusion in the case of several space variables

A. V. Nesterov

Plekhanov Russian University of Economics, 117997, Moscow, Russia
Full-text PDF
DOI: https://doi.org/10.31857/S0044466924030128
Abstract: A formal asymptotic expansion is constructed for the solution of the Cauchy problem for a singularly perturbed operator differential transport equation with small nonlinearities and weak diffusion in the case of several space variables. Under the conditions imposed on the data of the problem, the leading asymptotic term is described by the multidimensional generalized Burgers–Korteweg–de Vries equation. Under certain conditions, the remainder is estimated with respect to the residual.
Key words: small parameter, singular perturbations, asymptotic expansion, generalized multidimensional Burgers–Korteweg–de Vries equation.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSSW-2023-0004
This study was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the state assignment on the subject “Artificial intelligence models, methods, and algorithms in economics problems for analysis and stylization of multidimensional data, prediction of time series, and design of recommender systems”, project no. FSSW-2023-0004.
Received: 10.10.2023
Revised: 12.11.2023
Accepted: 17.11.2023
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 3, Pages 490–496
DOI: https://doi.org/10.1134/S0965542524030114
Bibliographic databases:
Document Type: Article
UDC: 517.955.8 + 519.633
Language: Russian
Citation: A. V. Nesterov, “On asymptotics of the solution to the Cauchy problem for a singularly perturbed operator-differential transport equation with weak diffusion in the case of several space variables”, Zh. Vychisl. Mat. Mat. Fiz., 64:3 (2024), 526–533; Comput. Math. Math. Phys., 64:3 (2024), 490–496
Citation in format AMSBIB
\Bibitem{Nes24}
\by A.~V.~Nesterov
\paper On asymptotics of the solution to the Cauchy problem for a singularly perturbed operator-differential transport equation with weak diffusion in the case of several space variables
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 3
\pages 526--533
\mathnet{http://mi.mathnet.ru/zvmmf11723}
\crossref{https://doi.org/10.31857/S0044466924030128}
\elib{https://elibrary.ru/item.asp?id=73160220}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 3
\pages 490--496
\crossref{https://doi.org/10.1134/S0965542524030114}
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