Full paper in PDF format:
$%J. L. Boldrini, E. Fernández-Cara, and M. A. Rojas-Medar, An optimal control problem for a generalized Boussinesq model: The time dependent case, Rev. Mat. Complut. 20 (2007), no. 2, 339–366.%$

An Optimal Control Problem for a Generalized Boussinesq Model: The Time Dependent Case
Jose Luiz BOLDRINI, Enrique FERNÁNDEZ-CARA,
and Marko Antonio ROJAS-MEDAR
Department of Mathematics
IMECC-UNICAMP, CP 6065, 130813-859
Campinas-SP — Brazil
boldrini@ime.unicamp.br
Department of Differential Equations
and Numerical Analysis
University of Sevilla, Aptdo. 1160
41080 Sevilla — Spain
cara@us.es
Department of Applied Mathematics
IMECC-UNICAMP, CP 6065, 13083-859
Campinas-SP — Brazil
marko@ime.unicamp.br

Received: January 9, 2006
Accepted: January 15, 2007

ABSTRACT

We consider an optimal control problem governed by a system of nonlinear partial differential equations modelling viscous incompressible flows submitted to variations of temperature. We use a generalized Boussinesq approximation. We obtain the existence of the optimal control as well as first order optimality conditions of Pontryagin type by using the Dubovitskii-Milyutin formalism.

Key words: optimal control, Boussinesq model, Dubovitskii-Milyutin formalism.
2000 Mathematics Subject Classification: 49J20, 76D03.