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Theses

Etude de quelques E.D.P. non linéaires dans L^1 avec des conditions générales sur le bord

Abstract : This thesis is devoted to the study of various problems of nonlinear partial differential equations of elliptic-parabolic type and of hyperbolic type. These equations are not generally well-posed within the framework of weak solutions (i.e. in distributions
sense), because in general there is no uniqueness. Formulations more suitable were introduced: solutions called SOLA, entropy solutions and renormalized solutions. This thesis, made up of five
chapters, gives results of existence and uniqueness of entropy and renormalized solutions for four nonlinear problems. After recalling some definitions and results necessary for our work, we prove in chapter 2 the existence and the uniqueness of an entropy solution to an elliptic problem of diffusion-convection type with nonlinear boundary conditions including the usual boundary conditions. In
chapter 3, existence and uniqueness of an entropy solution of a parabolic problem with absorption depending on space variable are shown. Chapter 4 deals with the existence of renormalized solutions
for a nonlinear Stefan problem. The last result, presented in chapter 5, concerns the existence and the uniqueness of an entropy solution for a conservation laws problem with nonlinear boundary
conditions.
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Submitted on : Saturday, October 28, 2006 - 8:19:01 PM
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Karima Sbihi. Etude de quelques E.D.P. non linéaires dans L^1 avec des conditions générales sur le bord. Mathématiques [math]. Université Louis Pasteur - Strasbourg I, 2006. Français. ⟨NNT : 2006STR13111⟩. ⟨tel-00110417⟩

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