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Issue		ESAIM: COCV Volume 5, 2000
Page(s)		477 - 500
DOI		10.1051/cocv:2000118

DOI: 10.1051/cocv:2000118

ESAIM: COCV, October 2000, Vol. 5, 477-500

Optimal control of stationary, low Mach number,
highly nonisothermal, viscous flows

Max D. Gunzburger
Department of Mathematics, Iowa State University, Ames IA 50011-2064, U.S.A.;
(gunzburg@iastate.edu)

O.Yu. Imanuvilov
Department of Mathematics, Iowa State University, Ames IA 50011-2064, U.S.A.;
(vika@iastate.edu)

Received January 31, 2000.

Abstract: An optimal control problem for a model for stationary, low Mach number, highly nonisothermal, viscous flows is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. The existence of solutions of a boundary value problem for the model equations is established as is the existence of solutions of the optimal control problem. Then, a derivation of an optimality system, i.e., a boundary value problem from which the optimal control and state may be determined, is given.

Résumé: Dans cet article, on considère un problème de contrôle optimal pour un fluide visqueux, stationnaire et fortement non-isothermique, à petit nombre de Mach. On regarde d'abord un problème de minimisation pour l'écart entre le champ de vitesse et un champ de vitesse donné. On montre l'existence de solutions pour ce problème ainsi que pour le problème de contrôle optimal initial. On donne ensuite un système vérifié par les solutions du probléme de contrôle optimal, système qui consiste en un problème aux limites dont on peut obtenir le contrôle optimal et l'état.

Keywords and phrases: Optimal control, compressible flows, viscous flows, low Mach number flows.

AMS Subject Classification: 49J20, 49K20, 76N99

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