Study of some Nonlinear Problems for Partial Differential Equations and Fractional with Non-Local Conditions
This thesis is devoted to the study of some classical and fractional nonlinear parabolic problemswith different boundary conditions.
We started the first chapter of this thesis with reminders of some fundamental preliminary concepts andthe tools needed for this work.
The second chapter is devoted to studying the existence and uniqueness of a weak solution of anonlinear parabolic problem with an integral condition and a Neumann condition. Where, we show theexistence and uniqueness of the strong solution for the linear problem by the method of energy inequality.
Then, applying an iterative process based on the results obtained for the linear problem, we prove theexistence and the uniqueness of the weak solution of the nonlinear problem.
The third chapter is devoted to the solvability of the weak solution and the blow up solution in finitetime of a problem for a class of semi linear parabolic equations with an integral condition of second type.
In the fourth chapter, we study a mixed problem related to a nonlinear fractional parabolic equationwith a classical Neumann condition and an integral condition by the energy inequality method for the linearproblem and by the linearization method for the non-linear problem.
Finally, in the fifth chapter, the existence and uniqueness of a weak solution of the Dirichlet
problem for a class of semi-linear parabolic equations by the Faedo-Galerkin method was examined.
Keywords - Nonlinear parabolic equations, Fractional equations, Functional spaces, Energy inequality, Faedo-Galerkin method, Fixed point theorem, Sturm Liouville problem, Blow up solution, Integralconditions.