Abstract:
The global solvability of the inhomogeneous mixed boundary value problem and control problems for the reaction–diffusion–convection equation are proved in the case when the reaction coefficient nonlinearly depends on the concentration. The maximum and minimum principles are established for the solution of the boundary value problem. The optimality systems are derived and the local stability estimates of optimal solutions are established for control problems with specific reaction coefficients.
Keywords:
nonlinear reaction–diffusion–convection equation, mixed boundary conditions, maximum principle, control problems, optimality systems, local stability estimates.
The work was carried out within the framework
of the state assignment of the Institute of Applied Mathematics, FEB RAS
(Theme no. 075-01095-20-00).
Received: 10.03.2021 Received in revised form: 05.04.2021 Accepted: 20.05.2021
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: English
Citation:
Gennady V. Alekseev, Roman V. Brizitskii, “Analysis of the boundary value and control problems for nonlinear reaction–diffusion–convection equation”, J. Sib. Fed. Univ. Math. Phys., 14:4 (2021), 452–462
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\paper Analysis of the boundary value and control problems for nonlinear reaction--diffusion--convection equation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2021
\vol 14
\issue 4
\pages 452--462
\mathnet{http://mi.mathnet.ru/jsfu930}
\crossref{https://doi.org/10.17516/1997-1397-2021-14-4-452-462}
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Linking options:
https://www.mathnet.ru/eng/jsfu930
https://www.mathnet.ru/eng/jsfu/v14/i4/p452
This publication is cited in the following 4 articles:
R. V. Brizitskii, A. A. Donchak, “Multiplicative Control Problem for a Nonlinear Reaction–Diffusion Model”, Comput. Math. and Math. Phys., 64:1 (2024), 56
Gennadii Alekseev, Olga Soboleva, “Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer”, Mathematics, 12:3 (2024), 391
R. V. Brizitskii, A. A. Donchak, “Zadacha multiplikativnogo upravleniya dlya nelineinoi modeli reaktsii–diffuzii”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:1 (2024)
Jun Moon, “A Pontryagin maximum principle for terminal state-constrained optimal control problems of Volterra integral equations with singular kernels”, MATH, 8:10 (2023), 22924
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