Homogénéisation et Controle Optimal pour des Problèmes de Stokes et pour un Problème de Torsion Elastique

Abstract : This thesis is devoted to the study of optimal control and homogenization for some problems associated to the Stokes equation and also for an elastic torsion problem. For each of the problems, a control act on the state equation. This control belongs to a set of admissible controls. We consider a cost function which depends on the state and on the control. The control optimal (unique) is the function in the set of admissible controls which minimizes the cost function. Then we study its behaviour. If it admits a limit, we characterize it as an optimal control associated to the homogenized problem . At first , we study an optimal control problem in a mixture of two fluids. Those fluids are distributed periodically in a bi or three-dimensionnal domain. Each fluids obeys the Stokes equations. Then, we study also a mixture of two fluids but separated by an rapidly oscillating interface. These fluids obeys The Stokes equations. We then study an optimal control problem for the Stokes equations in perforated domains. We suppose that the size of the perforations is smaller than a given period. Finally, we study the optimal control of an elastic torsion problem. For each of these parts, we characterize the limit of the optimal control as the optimal control of the limit problem.
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Theses
Mathematics [math]. Université de Metz, 2001. French


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Contributor : Hakima Zoubairi <>
Submitted on : Friday, March 29, 2002 - 11:18:25 AM
Last modification on : Friday, March 29, 2002 - 11:18:25 AM

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Hakima Zoubairi. Homogénéisation et Controle Optimal pour des Problèmes de Stokes et pour un Problème de Torsion Elastique. Mathematics [math]. Université de Metz, 2001. French. <tel-00001290>

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