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Étude des équations des milieux poreux et des modèles de cloques

Abstract : In this thesis, we study two completely independent problems. The first one focuses on a simple mathematical model of thin films delamination and blistering analysis. In the second one, we are interested in the study of the porous medium equation motivated by seawater intrusion problems. In the first part of this work, we consider a simple one-dimensional variational model, describing the delamination of thin films under cooling. We characterize the global minimizers, which correspond to films of three possible types : non delaminated, partially delaminated (called blisters), or fully delaminated. Two parameters play an important role : the length of the film and the cooling parameter. In the phase plane of those two parameters, we classify all the minimizers. As a consequence of our analysis, we identify explicitly the smallest possible blisters for this model. In the second part, we answer a long standing open question about the existence of new contractions for porous medium type equations. For m>0, we consider nonnegative solutions U(t,x) of the following equationU_t=Delta U^m.For 0
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Ghada Chmaycem. Étude des équations des milieux poreux et des modèles de cloques. Mathématiques générales [math.GM]. Université Paris-Est, 2014. Français. ⟨NNT : 2014PEST1080⟩. ⟨tel-01127042⟩



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