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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 1, Pages 76–101 (Mi timm530)  

This article is cited in 7 scientific papers (total in 7 papers)

Optimal boundary control of a system describing thermal convection

A. I. Korotkii, D. A. Kovtunov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A problem of optimal boundary control of thermal sources for a stationary model of natural thermal convection of a high-viscosity inhomogeneous incompressible fluid in the Boussinesq approximation is investigated. Some conditions for the solvability of the problem are given; necessary and sufficient optimality conditions are specified. Optimality conditions and the corresponding conjugate problems defining the gradient of the quality functional are written for a number of particular cases of the functional. Procedures for the numerical finding of an optimal control based on gradient methods are described. The results of numerical experiments are given.

Keywords: optimal control, thermal convection, gradient method.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 272, suppl. 1, S74–S100

Bibliographic databases:

UDC: 534.4+517.9
Received: 04.09.2009

Citation: A. I. Korotkii, D. A. Kovtunov, “Optimal boundary control of a system describing thermal convection”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 76–101; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S74–S100

Citation in format AMSBIB
\by A.~I.~Korotkii, D.~A.~Kovtunov
\paper Optimal boundary control of a~system describing thermal convection
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 1
\pages 76--101
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 272
\issue , suppl. 1
\pages S74--S100

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    This publication is cited in the following articles:
    1. A. I. Korotkii, D. A. Kovtunov, “Optimalnoe upravlenie teplovoi konvektsiei”, Tr. IMM UrO RAN, 16, no. 5, 2010, 103–112  mathnet  elib
    2. G. V. Alekseev, M. A. Shepelov, “On the stability of solutions to coefficient inverse extreme problems for the stationary convection-diffusion equation”, J. Appl. Industr. Math., 7:1 (2013), 1–14  mathnet  crossref  mathscinet
    3. G. V. Alekseev, R. V. Brizitskii, Zh. Yu. Saritskaya, “Stability estimates of solutions to extremal problems for a nonlinear convection-diffusion-reaction equation”, J. Appl. Industr. Math., 10:2 (2016), 155–167  mathnet  crossref  crossref  mathscinet  elib
    4. R. V. Brizitskii, Zh. Yu. Saritskaya, “Inverse coefficient problems for a non-linear convection–diffusion–reaction equation”, Izv. Math., 82:1 (2018), 14–30  mathnet  crossref  crossref  adsnasa  isi  elib
    5. A. I. Korotkii, I. A. Tsepelev, “Vosstanovlenie parametrov techeniya vyazkoi teploprovodnoi zhidkosti po nekotorym izmereniyam na ee poverkhnosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:1 (2018), 27–36  mathnet  crossref  elib
    6. R. V. Brizitskii, Zh. Yu. Saritskaya, “Boundary control problem for a nonlinear convection-diffusion-reaction equation”, Comput. Math. Math. Phys., 58:12 (2018), 2053–2063  mathnet  crossref  crossref  isi  elib
    7. R. V. Brizitskii, Zh. Yu. Saritskaya, R. R. Kravchuk, “Boundary value and extremum problems for generalized Oberbeck–Boussinesq model”, Sib. elektron. matem. izv., 16 (2019), 1215–1232  mathnet  crossref
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