Etude de quelques problèmes de Cauchy inverses.

Abstract

The goal of this work is the study of a class of inverse Cauchy problems. A new regularization method based on the well-known method of regularization by truncation of eliminating all high frequencies in the solution of ill-posed problem by making an appropriate rule for choosing the regularization parameter is proposed to develop. This will provide an a posteriori estimate between the exact solution and regularized approximation. We establish necessary and sufficient conditions of existence of the solution and under certain conditions, we give stability and convergence results and error rates. Finally, we present some numerical applications which show the effectiveness of the proposed method.