Quelques problèmes d'homogénéisation à faible et fort contraste

Abstract : This thesis is devoted to the homogenization of conduction and linearized elasticity equations in dimensions 2 and 3. In dimension 2, we first consider the homogenization of the Hall effect which can be seen as a low contrast problem. Then we study the inverse case of high contrast problems. We establish compacity and duality results for sequences of conductivities which are not necessarily symmetric and not uniformly bounded from below or from above. In dimension 3, we are interested in non periodic fibered microstructures. On the one hand, using the small amplitude homogenization procedure of Tartar, we obtain some homogenized models in conduction and in isotropic elasticity. Moreover, we extend the results of Tartar to the anisotropic elasticity, which permits to derive a simplified model. On the other hand, in high contrast homogenization, we obtain a model in the case where the external medium has a low conductivity.
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Submitted on : Monday, December 17, 2007 - 1:31:00 PM
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David Manceau. Quelques problèmes d'homogénéisation à faible et fort contraste. Mathématiques [math]. Université Rennes 1, 2007. Français. ⟨tel-00198459⟩

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