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Tr. Mosk. Mat. Obs., 2019, Volume 80, Issue 2, Pages 259–274 (Mi mmo627)  

Control with point observation for a parabolic problem with convection

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

a Economical and Mathematical Faculty, Plekhanov Russian University of Economics, Moscow, Russia 113054
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia, 119234
c FITO-AGRO, Moskovsky 35-12, Moscow, Russia
d Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia 105005

Abstract: We consider a control problem related to the mathematical model of temperature control in industrial hothouses. It is based on a one-dimensional non-selfadjoint parabolic equation with variable coefficients. Defining an optimal control as a minimizing function for a quadratic functional, we study its qualitative properties and the structure of the set of admissible temperature functions. We prove controllability for a certain family of control functions.

Key words and phrases: Parabolic equation, extremum problem, quadratic functional, minimizing function, controllability, exact controllability.

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English version:
Transactions of the Moscow Mathematical Society, 2019, 80, 221–234

UDC: 517.977.56, 517.977.57, 517.956.4
MSC: 35K20, 35Q79, 35Q93, 49J20
Received: 20.06.2019

Citation: I. V. Astashova, D. A. Lashin, A. V. Filinovskii, “Control with point observation for a parabolic problem with convection”, Tr. Mosk. Mat. Obs., 80, no. 2, MCCME, M., 2019, 259–274; Trans. Moscow Math. Soc., 80 (2019), 221–234

Citation in format AMSBIB
\Bibitem{AstLasFil19}
\by I.~V.~Astashova, D.~A.~Lashin, A.~V.~Filinovskii
\paper Control with point observation for a parabolic problem with convection
\serial Tr. Mosk. Mat. Obs.
\yr 2019
\vol 80
\issue 2
\pages 259--274
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo627}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2019
\vol 80
\pages 221--234
\crossref{https://doi.org/10.1090/mosc/296}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85083794751}


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