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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 11, Pages 1851–1860
DOI: https://doi.org/10.31857/S0044466922110138 (Mi zvmmf11470) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Partial Differential Equations

Asymptotic solution of the boundary control problem for a Burgers-type equation with modular advection and linear gain

V.T. Volkov, N. N. Nefedov

Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
Citations (5)
DOI: https://doi.org/10.31857/S0044466922110138
Abstract: A singularly perturbed periodic problem for a parabolic reaction–diffusion–advection Burgers-type equation with modular advection and linear gain is considered. Conditions for the existence, uniqueness, and asymptotic Lyapunov stability of a periodic solution with an internal transition layer are obtained, and its asymptotic approximation is constructed. Asymptotic analysis is applied in solving the boundary control problem to achieve the required law of front’s motion. The concept of an asymptotic solution of this problem is formulated, sufficient conditions for the existence and uniqueness of the solution are obtained, and an asymptotic approximation of the solution is constructed.
Key words: singularly perturbed parabolic equations, periodic problems, reaction–diffusion equations, contrast structures, inner layers, fronts, asymptotic, methods, differential inequalities, asymptotic Lyapunov stability, Burgers equations with modular advection, inverse coefficient problem, asymptotic solution of inverse problem.
Funding agency Grant number
Russian Science Foundation 18-11-00042
This work was supported by the Russian Science Foundation (project no. 18-11-00042).
Received: 15.10.2021
Revised: 04.04.2022
Accepted: 08.06.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 11, Pages 1849–1858
DOI: https://doi.org/10.1134/S0965542522110112
Bibliographic databases:
Document Type: Article
UDC: 519.956.4
Language: Russian
Citation: V.T. Volkov, N. N. Nefedov, “Asymptotic solution of the boundary control problem for a Burgers-type equation with modular advection and linear gain”, Zh. Vychisl. Mat. Mat. Fiz., 62:11 (2022), 1851–1860; Comput. Math. Math. Phys., 62:11 (2022), 1849–1858
Citation in format AMSBIB
\Bibitem{VolNef22}
\by V.T.~Volkov, N.~N.~Nefedov
\paper Asymptotic solution of the boundary control problem for a Burgers-type equation with modular advection and linear gain
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 11
\pages 1851--1860
\mathnet{http://mi.mathnet.ru/zvmmf11470}
\crossref{https://doi.org/10.31857/S0044466922110138}
\elib{https://elibrary.ru/item.asp?id=49455078}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 11
\pages 1849--1858
\crossref{https://doi.org/10.1134/S0965542522110112}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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