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Homogénéisation d'une classe de problèmes non linéaires avec des conditions de Fourier dans des ouverts perforés

Abstract : This thesis is devoted to the homogenization of an elliptic quasi-linear problem in a perforated domain with Fourier conditions on boundary of the holes. First, the Results of hornogenization that we obtain generalize anterior results of Cioranescu-Donato because the coefficients aij depend on the solution, what prevent us of passing directly to the lirnit on sorne terrns. ln addition to the homogenization results, a theorem of existence and uniqueness of the solution is proved. ln the second chapter, we studied the limit behavior the solution of the same problem but in weakly connected domains, the homogenization results are proved in three different geometries according to the connectedness of materials and according to the size of the bridges. ln the last chapter, a numerical method is developed to calculate explicitly the homogenized coefficients established before, the non linear problem is approached by a suite of linears problems by using an iterative method.
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Salaheddine Bendib. Homogénéisation d'une classe de problèmes non linéaires avec des conditions de Fourier dans des ouverts perforés. Autre [cs.OH]. Institut National Polytechnique de Lorraine, 2004. Français. ⟨NNT : 2004INPL079N⟩. ⟨tel-01749821⟩

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