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Boundary Control Problem for a Nonlinear Convection–Diffusion–Reaction Equation

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Abstract

The solvability of boundary-value and extremum problems for a nonlinear convection–diffusion–reaction equation with mixed boundary conditions is proved in the case where the coefficient in the boundary condition is a fairly arbitrary function of the solution to the boundary value problem. For the mass transfer coefficient equal to the modulus of the substance concentration, local stability estimates of the solution to the extremum problem with respect to relatively small perturbations in the cost functional and the given functions of the boundary value problem are obtained.

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ACKNOWLEDGMENTS

The first author’s work was supported by the Federal Agency of Scientific Organizations within the framework of the state assignment (topic no. 0263-2018-0001). The second author acknowledges the support of the Russian Foundation for Basic Research (project no. 16-01-00365-a) and the Basic Research Program “Far East” of the Far Eastern Branch of the Russian Academy of Sciences (project no. 18-5-064).

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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, 690091, Vladivostok, Russia

    R. V. Brizitskii & Zh. Yu. Saritskaya

Authors
  1. R. V. Brizitskii
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  2. Zh. Yu. Saritskaya
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Correspondence to R. V. Brizitskii or Zh. Yu. Saritskaya.

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Translated by I. Ruzanova

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Brizitskii, R.V., Saritskaya, Z.Y. Boundary Control Problem for a Nonlinear Convection–Diffusion–Reaction Equation. Comput. Math. and Math. Phys. 58, 2053–2063 (2018). https://doi.org/10.1134/S0965542518120060

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  • DOI: https://doi.org/10.1134/S0965542518120060

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