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Multiplicative Control Problem for a Nonlinear Reaction–Diffusion Model

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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.

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Funding

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).

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia

    R. V. Brizitskii

  2. Far Eastern Federal University, 690922, Vladivostok, Russia

    R. V. Brizitskii & A. A. Donchak

Authors
  1. R. V. Brizitskii
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  2. A. A. Donchak
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Correspondence to R. V. Brizitskii or A. A. Donchak.

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Translated by E. Chernokozhin

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Brizitskii, R.V., Donchak, A.A. Multiplicative Control Problem for a Nonlinear Reaction–Diffusion Model. Comput. Math. and Math. Phys. 64, 56–72 (2024). https://doi.org/10.1134/S0965542524010056

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  • DOI: https://doi.org/10.1134/S0965542524010056

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