Geodesic
Optimal boundary control of a~system describing thermal convection
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 76-101

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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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     author = {A. I. Korotkii and D. A. Kovtunov},
     title = {Optimal boundary control of a~system describing thermal convection},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a7/}
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A. I. Korotkii; D. A. Kovtunov. Optimal boundary control of a~system describing thermal convection. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 1, pp. 76-101. http://geodesic.mathdoc.fr/item/TIMM_2010_16_1_a7/