## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2011 (2011), Article ID 535736, 28 pages.

### Stability of Optimal Controls for the Stationary Boussinesq Equations

Gennady Alekseev and Dmitry Tereshko

#### 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.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2011 (2011), Article ID 535736, 28 pages.

**Dates**

Received: 26 May 2011

Accepted: 3 August 2011

First available in Project Euclid: 25 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1485313250

**Digital Object Identifier**

doi:10.1155/2011/535736

**Mathematical Reviews number (MathSciNet)**

MR2847599

**Zentralblatt MATH identifier**

1236.49064

#### Citation

Alekseev, Gennady; Tereshko, Dmitry. Stability of Optimal Controls for the Stationary Boussinesq Equations. Int. J. Differ. Equ. 2011 (2011), Article ID 535736, 28 pages. doi:10.1155/2011/535736. https://projecteuclid.org/euclid.ijde/1485313250