Identification of Initial Condition in Parabolic Convection Diffusion Equation Using Radial Basis Function Partition of Unity

Identification of Initial Condition in a Parabolic Convection Diffusion Equation

Résumé

The present paper deals with the identification problem of an unknown initial condition in convection diffusion equation. This inverse problem is transformed into a constrained optimization problem. We prove its solution existence. The radial basis function based partition of unity is considered as a discretization method. The obtained matrix system is solved via a robust approach based on preconditioning techniques. Using the quasi Newton algorithm we approach the solution of the optimization problem. At the end, we establish several numerical examples in order to illustrate our theoretical results and the validity of the constructed numerical scheme.