ITERATIVE REGULARIZATION METHOD FOR AN ABSTRACT INVERSE GOURSAT PROBLEM
Loading...
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Khayyam Journal of Mathematics
Abstract
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.
Description
no. 2, 279-297
DOI: 10.22034/KJM.2020.237076.1900