Quasi solution of a backward space fractional diffusion equation

• Published in: Journal of inverse and ill-posed problems Vol. 27; no. 6; pp. 795 - 814
• Main Authors: Salehi Shayegan, Amir Hossein, Zakeri, Ali
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.12.2019; Walter de Gruyter GmbH
• Subjects: 35R11; 65N21; Backward space fractional diffusion equation; Existence theorems; Finite element method; Ill posed problems; Linear equations; quasi solution; Regularization; stability; TSVD regularization; Uniqueness theorems

In this paper, based on a quasi solution approach, i.e., a methodology involving minimization of a least squares cost functional, we study a backward space fractional diffusion equation. To this end, we give existence and uniqueness theorems of a quasi solution in an appropriate class of admissible...