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On Problems of Extremum and Estimates of Control Function for Parabolic Equation

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Moscow University Mathematics Bulletin Aims and scope

Abstract

We consider an extremum problem associated with a mathematical model of the temperature control. It is based on a one-dimensional non-self-adjoint parabolic equation of general form. Determining the optimal control as a function minimizing the weighted quadratic functional, we prove the existence of a solution to the problem of the double minimum by control and weight functions. We also obtain upper estimates for the norm of the control function in terms of the value of the functional. These estimates are used to prove the existence of the minimizing function for unbounded sets of control functions.

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Funding

The work is partially supported by the Russian Science Foundation, project no. 20-11-20272.

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Authors and Affiliations

  1. Chair of Differential Equations, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    I. V. Astashova & A. V. Filinovskiy

  2. Chair of Higher Mathematics, Plekhanov Russian University of Economics, Moscow, Russia

    I. V. Astashova

  3. Scientific and Production Company FITO, Moscow, Russia

    D. A. Lashin

  4. Chair of Higher Mathematics, Faculty of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia

    A. V. Filinovskiy

Authors
  1. I. V. Astashova
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  2. D. A. Lashin
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  3. A. V. Filinovskiy
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Correspondence to I. V. Astashova, D. A. Lashin or A. V. Filinovskiy.

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The authors of this work declare that they have no conflicts of interest.

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Translated by E. Oborin

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Astashova, I.V., Lashin, D.A. & Filinovskiy, A.V. On Problems of Extremum and Estimates of Control Function for Parabolic Equation. Moscow Univ. Math. Bull. 79, 44–54 (2024). https://doi.org/10.3103/S0027132224700050

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