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

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 3, page 840-863
- ISSN: 1292-8119

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topRavindran, S. S.. "Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method." ESAIM: Control, Optimisation and Calculus of Variations 20.3 (2014): 840-863. <http://eudml.org/doc/272927>.

@article{Ravindran2014,

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.},

author = {Ravindran, S. S.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {boundary penalty; dirichlet boundary control; Navier–stokes type system; soret convection; Navier-Stokes type system; Soret convection; Dirichlet boundary control},

language = {eng},

number = {3},

pages = {840-863},

publisher = {EDP-Sciences},

title = {Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method},

url = {http://eudml.org/doc/272927},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Ravindran, S. S.

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 3

SP - 840

EP - 863

AB - 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.

LA - eng

KW - boundary penalty; dirichlet boundary control; Navier–stokes type system; soret convection; Navier-Stokes type system; Soret convection; Dirichlet boundary control

UR - http://eudml.org/doc/272927

ER -

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