Iterative regularization method for an abstract inverse Goursat problem

Document Type : Original Article

Authors

Mohamed Sief Eddine Meziani ¹

Nadjib Boussetila ²

Faouzia Rebbani ³

Abderafik Benrabah ⁴

¹ Ecole Normale Supérieure de l'Enseignement Technologique, Azzaba, Skikda, Algeria. Applied Mathematics Laboratory, University Badji Mokhtar Annaba.

² Department of Mathematics, 8 Mai 1945 Guelma University, P.O.Box 401, Guelma 24000, Algeria

³ Ecole Supérieure de Technologies Industrielles, Annaba, Algeria. Applied Mathematics Laboratory, University Badji Mokhtar Annaba.

⁴ University 8 Mai 1945 Guelma, Algeria. Applied Mathematics Laboratory, University Badji Mokhtar Annaba.

10.22034/kjm.2020.237076.1900

Abstract

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.

Keywords

Ill-posed problems

Goursat problem

Iterative regularization

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