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Optimal boundary control of a system describing thermal convection

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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. Conditions for the solvability of the problem, as well as necessary and sufficient optimality conditions, are specified. Optimality conditions and the corresponding adjoint problems defining the gradient of the quality functional are written for several special cases of the functional. Computational procedures for finding an optimal control based on gradient methods are described. The results of numerical experiments are given.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    A. I. Korotkii & D. A. Kovtunov

Authors
  1. A. I. Korotkii
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  2. D. A. Kovtunov
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Correspondence to A. I. Korotkii.

Additional information

Original Russian Text © A.I. Korotkii, D.A. Kovtunov, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 1.

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Korotkii, A.I., Kovtunov, D.A. Optimal boundary control of a system describing thermal convection. Proc. Steklov Inst. Math. 272 (Suppl 1), 74–100 (2011). https://doi.org/10.1134/S0081543811020076

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