Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2024, Number 1, Pages 40–50
DOI: https://doi.org/10.55959/vmumm4587 (Mi vmumm4587) 		 
Mathematics

Extremum problems and control function estimates for a parabolic equation

I. V. Astashovaab, D. A. Lashinc, A. V. Filinovskiiad

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow
b Plekhanov Russian State University of Economics, Moscow
c Company "Fito", Moscow, Sosenskoye
d Bauman Moscow State Technical University
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DOI: https://doi.org/10.55959/vmumm4587
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 obtained 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.
Key words: parabolic equation, extremum problem, weight quadratic functional, minimizing function, double minimum, upper estimates, unbounded set of control functions.
Funding agency Grant number
Russian Science Foundation 20-11-20272
The work is partially supported by the Russian Science Foundation, project no. 20-11-20272.
Received: 23.11.2023
English version:
Moscow University Mathematics Bulletin, 2024, Volume 79, Issue 1, Pages 44–54
DOI: https://doi.org/10.3103/S0027132224700050
Bibliographic databases:
Document Type: Article
UDC: 517.977.56, 517.977.57, 517.956.4
Language: Russian
Citation: I. V. Astashova, D. A. Lashin, A. V. Filinovskii, “Extremum problems and control function estimates for a parabolic equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 1, 40–50; Moscow University Mathematics Bulletin, 79:1 (2024), 44–54
Citation in format AMSBIB
\Bibitem{AstLasFil24}
\by I.~V.~Astashova, D.~A.~Lashin, A.~V.~Filinovskii
\paper Extremum problems and control function estimates for a parabolic equation
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2024
\issue 1
\pages 40--50
\mathnet{http://mi.mathnet.ru/vmumm4587}
\crossref{https://doi.org/10.55959/vmumm4587}
\elib{https://elibrary.ru/item.asp?id=62487643}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2024
\vol 79
\issue 1
\pages 44--54
\crossref{https://doi.org/10.3103/S0027132224700050}
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