Abstract
The global solvability of boundary value problems for the reaction–diffusion–convection equation is proved for the case in which the reaction coefficient in the equation and the mass transfer coefficient in the boundary condition nonlinearly depend on the substance concentration. The minimum and maximum principle for the concentration is established. The solvability of multiplicative control problems is proved in general form. Optimality systems are derived and the presence of the bang-bang principle is established for extremum problems under the assumption that the performance functionals and the solution-dependent coefficients of the model are Fréchet differentiable.
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Funding
The research by R.V. Brizitskii and Zh.Yu. Saritskaia was carried out in the framework of the State Order for the Institute of Applied Mathematics of the Far East Branch of the Russian Academy of Sciences, topic no. 075-01095-20-00. The research by V.S. Bystrova was supported by the RF Ministry for Science and Higher Education, project no. 075-15-2019-1878.
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Translated by V. Potapchouck
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Brizitskii, R.V., Bystrova, V.S. & Saritskaia, Z.Y. Analysis of Boundary Value and Extremum Problems for a Nonlinear Reaction–Diffusion–Convection Equation. Diff Equat 57, 615–629 (2021). https://doi.org/10.1134/S0012266121050062
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DOI: https://doi.org/10.1134/S0012266121050062