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Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method

Published online by Cambridge University Press:  05 June 2014

S.S. Ravindran
S.S. Ravindran*
Affiliation:
Department of Mathematical Sciences, 201C Shelby Center for Science and Technology, The University of Alabama in Huntsville, Huntsville, AL 35899, USA. ravinds@uah.edu
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Abstract

In this paper, we study the boundary penalty method for optimal control of unsteady Navier–Stokes type system that has been proposed as an alternative for Dirichlet boundary control. Existence and uniqueness of solutions are demonstrated and existence of optimal control for a class of optimal control problems is established. The asymptotic behavior of solution, with respect to the penalty parameter ϵ, is studied. In particular, we prove convergence of solutions of penalized control problem to the corresponding solutions of the Dirichlet control problem, as the penalty parameter goes to zero. We also derive an optimality system and determine optimal solutions. In order to illustrate the theoretical results and the practical utility of control, we numerically address the problem of controlling unsteady convection with Soret effect using a gradient-based method. Numerical results show the effectiveness of the approach.

Keywords

Boundary penaltydirichlet boundary controlNavier–stokes type systemsoret convection
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 3 , July 2014 , pp. 840 - 863
Copyright
© EDP Sciences, SMAI 2014

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