%0 Journal Article %T Iterative regularization method for an abstract inverse Goursat problem %J Khayyam Journal of Mathematics %I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures) %Z 2423-4788 %A Meziani, Mohamed Sief Eddine %A Boussetila, Nadjib %A Rebbani, Faouzia %A Benrabah, Abderafik %D 2021 %\ 07/01/2021 %V 7 %N 2 %P 279-297 %! Iterative regularization method for an abstract inverse Goursat problem %K ill-posed problems %K Goursat problem %K Iterative regularization %R 10.22034/kjm.2020.237076.1900 %X In this paper we deal with a problem of identification of an unknown source in the abstract inverse Goursat problem with two-time variables. We show that the considered problem is ill-posed according to the Hadamard sense. That is, the solution does not depend continuously on the data. In order to overcome the instability of the solution, we propose a regularization method via an iterative procedure, with the help of an extra measurement at an internal point. Some convergence results are established under a priori bound assumptions on the exact solution. Finally, numerical tests are presented to illustrate the accuracy and efficiency of the proposed regularization method. %U https://www.kjm-math.org/article_131345_efc2a63e428e10c33fdf6d2576031143.pdf