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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 504, Pages 28–31
DOI: https://doi.org/10.31857/S268695432203002X (Mi danma259) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

On the extremum control problem with pointwise observation for a parabolic equation

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

a Lomonosov Moscow State University, Moscow, Russia
b Plekhanov Russian State University of Economics, Moscow, Russia
c "FITO" Scientific Production Company, Moskovskii, Moscow oblast, Russia
d Bauman Moscow State Technical University, Moscow, Russia
Citations (2)
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DOI: https://doi.org/10.31857/S268695432203002X
Abstract: In this paper we consider a control problem with pointwise observation for a one-dimensional parabolic equation which arises in a mathematical model of climate control in industrial greenhouses. We study a general equation with variable diffusion coefficient, convection coefficient, and depletion potential. For the extremum problem of minimizing an integral weighted quadratic cost functional, we establish the existence and uniqueness of a minimizing function. We also study exact controllability and dense controllability of the problem. Necessary conditions for an extremum are obtained, and qualitative properties of the minimizing function are studied.
Keywords: parabolic equation, mixed problem, pointwise observation, extremum problem, exact controllability, dense controllability, necessary condition.
Presented: V. V. Kozlov
Received: 01.12.2021
Revised: 10.12.2021
Accepted: 14.03.2022
English version:
Doklady Mathematics, 2022, Volume 105, Issue 3, Pages 158–161
DOI: https://doi.org/10.1134/S1064562422030024
Bibliographic databases:
Document Type: Article
UDC: 517.956.4
Language: Russian
Citation: I. V. Astashova, D. A. Lashin, A. V. Filinovskii, “On the extremum control problem with pointwise observation for a parabolic equation”, Dokl. RAN. Math. Inf. Proc. Upr., 504 (2022), 28–31; Dokl. Math., 105:3 (2022), 158–161
Citation in format AMSBIB
\Bibitem{AstLasFil22}
\by I.~V.~Astashova, D.~A.~Lashin, A.~V.~Filinovskii
\paper On the extremum control problem with pointwise observation for a parabolic equation
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 504
\pages 28--31
\mathnet{http://mi.mathnet.ru/danma259}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4471700}
\elib{https://elibrary.ru/item.asp?id=48649151}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 3
\pages 158--161
\crossref{https://doi.org/10.1134/S1064562422030024}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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