Study Of Singular Anddegenrate Nonlinear Parabolic Problems With Different Boundary Conditions

Résumé: Partial differential equations with nonlocal boundary conditions occur increasingly in many fields of science and engineering. In this dissertation, we study two classes of nonlinear problems, the first one concerning a singular nonlinear parabolic problem with the classical Neumann boundary conditions with Bissel operator. When we show the existence and the uniqueness of weak solution by using the energy inequality and an iterative process based on a priori estimate. Then we use an explicite finite difference method to study the numerical solution for this problem. The second one related to a singular and degenerate nonlinear parabolic equation with integral conditions of second type. Where by using the energy inequality, variable separation and an iterative process based on a priori estimate we prove the existence and the uniqueness of weak solution for the nonlinear problem. After that we moved to dynamic issue, exactly we study the blow up solution of super-linear parabolic problem with nonlocal conditions and we give the numerical simulation of the blow up solution.

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