Homogénéisation et contrôle optimal pour des problèmes de Stokes et pour un problème de torsion élastique

Abstract : This thesis is devoted to the study of optimal control and homogeneization 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 wich 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. In the first part, 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 fluid obeys the Stokes equations. In the second part, we study also a mixture of two fluids but separated by an rapidly oscillating interface. These fluids obeys the Stoke equations. In the third part, we 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. In the last part, 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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Hakima Zoubairi. Homogénéisation et contrôle optimal pour des problèmes de Stokes et pour un problème de torsion élastique. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2001. Français. ⟨NNT : 2001METZ026S⟩. ⟨tel-01775441⟩

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