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International Journal of Differential Equations
Volume 2011 (2011), Article ID 535736, 28 pages
http://dx.doi.org/10.1155/2011/535736
Research Article

Stability of Optimal Controls for the Stationary Boussinesq Equations

Computational Fluid Dynamics Laboratory, Institute of Applied Mathematics FEB RAS, 7 Radio Street, Vladivostok 690041, Russia

Received 26 May 2011; Accepted 3 August 2011

Academic Editor: Yuji Liu

Copyright © 2011 Gennady Alekseev and Dmitry Tereshko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The stationary Boussinesq equations describing the heat transfer in the viscous heat-conducting fluid under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for temperature are considered. The optimal control problems for these equations with tracking-type functionals are formulated. A local stability of the concrete control problem solutions with respect to some disturbances of both cost functionals and state equation is proved.