Etude théorique et numérique de problèmes d'homogénéisation et de problèmes de contrôlabilité interne

Abstract : In the first part, we are interested in asymptotic behaviour of a thin tall strcture ( a tower) depending on three small parameters. The convergences of these small parameters for a Poisson's problem are studied : theoretically for a tridimensional tower and numerically for a biodimensional tower. In the last step, one can justify the use of a domains decomposition method. The second part is concerned with some numerical methods for internal controllability of linear or non-linear waves equations. The numerical methods, which are described, are : fixed point method and conjugate gradient, simulated annealing. In a second step, we apply the former methods for the partial internal exact controllability. To includes this work, we study an approached controllability for the solution of the waves equation. The exact control of some moments of this solution can be used to control the solution of the waves equation problem. To solve numerically this controllability problem, we use a fixed point method and a conjugate gradient algorithm
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Isabelle Charpentier. Etude théorique et numérique de problèmes d'homogénéisation et de problèmes de contrôlabilité interne. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1994. Français. ⟨NNT : 1994METZ050S⟩. ⟨tel-01776801⟩

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