Contrôlabilité de quelques systèmes gouvernés par des équations paraboliques

Abstract : This thesis is devoted to the study of the approximate and null controllability of linear parabolic systems on a nonempty bounded domain Ω of(), controlled by less controls than equations. The controls will be localized in an open set of Ω or on its boundary. We will study two different problems. The first of them involves controlling one of the equations indirectly with a coupling operator of order one. We obtain some results for different class of operators and systems. The second question we will study is to know if it is possible to control only some components of the solution of the system. We give a necessary and sufficient condition when the coupling coefficients are constant or time depending and study a simplified system when they are space dependent. We will finish by giving details on a numerical scheme with which we provide perspectives concerning some open problems in partial controllability of linear parabolic systems.
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Michel Duprez. Contrôlabilité de quelques systèmes gouvernés par des équations paraboliques. Géométrie algébrique [math.AG]. Université de Franche-Comté, 2015. Français. ⟨NNT : 2015BESA2038⟩. ⟨tel-01273789v2⟩

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