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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 1, Pages 77–93
DOI: https://doi.org/10.31857/S0044466924010077 (Mi zvmmf11691) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Optimal control

Multiplicative control problem for a nonlinear reaction–diffusion model

R. V. Brizitskiiab, A. A. Donchakb

a Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia
b Far Eastern Federal University, 690922, Vladivostok, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466924010077
Abstract: The paper studies a multiplicative control problem for the reaction–diffusion equation in which the reaction coefficient nonlinearly depends on the substance concentration, as well as on spatial variables. The role of multiplicative controls is played by the coefficients of diffusion and mass transfer. The solvability of the extremum problem is proved, and optimality systems are derived for a specific reaction coefficient. Based on the analysis of these systems, the relay property of multiplicative and distributed controls is established, and estimates of the local stability of optimal solutions to small perturbations of both the quality functionals and one of the given functions of the boundary value problem are derived.
Key words: nonlinear reaction–diffusion model, global solvability, maximum principle, multiplicative control problem, optimality system, relay property of controls, bang–bang principle, local stability estimates.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-01290-23-00
075-02-2023-946
This work was carried out as part of the state task of the Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences (No. 075-01290-23-00) and was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. 075-02-2023-946).
Received: 03.07.2023
Accepted: 16.09.2023
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 1, Pages 56–72
DOI: https://doi.org/10.1134/S0965542524010056
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: R. V. Brizitskii, A. A. Donchak, “Multiplicative control problem for a nonlinear reaction–diffusion model”, Zh. Vychisl. Mat. Mat. Fiz., 64:1 (2024), 77–93; Comput. Math. Math. Phys., 64:1 (2024), 56–72
Citation in format AMSBIB
\Bibitem{BriDon24}
\by R.~V.~Brizitskii, A.~A.~Donchak
\paper Multiplicative control problem for a nonlinear reaction–diffusion model
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 1
\pages 77--93
\mathnet{http://mi.mathnet.ru/zvmmf11691}
\crossref{https://doi.org/10.31857/S0044466924010077}
\elib{https://elibrary.ru/item.asp?id=68534078}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 1
\pages 56--72
\crossref{https://doi.org/10.1134/S0965542524010056}
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