Résumé:
In this thesis we present two fractional parabolic problems. In the first one, we treat the partial diffusion equation with an unknown boundary condition and a non-local coefficient. Using the Rothe method combined with the finite element method and an additional integral measure, we reconstruct the missing Dirichlet state. The presence of the non-local component leads to a large consuming of time when solving the equation numerically using the Newton method because the obtained Jacobian matrix is complete. In order to resolve these problems, we develop a method inspired from Gudi’s idea. The numerical experiment demonstrate the efficiency of the proposed approach.
Secondly, the well-posedness( existence, uniqueness and some stability results) of the problem concerning the reconstruction of the unknown time-dependent boundary function for ractional integro- ifferential equation, for this purpose, we use an additional integral measurement with Rothe time discretization. Finally, we give some numerical examples to illustrate the results.
