Stability of Optimal Controls for the Stationary Boussinesq EquationsReport as inadecuate

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International Journal of Differential EquationsVolume 2011 2011, Article ID 535736, 28 pages

Research ArticleComputational 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.


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

Author: Gennady Alekseev and Dmitry Tereshko



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