Quasi solution of a backward space fractional diffusion equation

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...

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Bibliographic Details
Published inJournal of inverse and ill-posed problems Vol. 27; no. 6; pp. 795 - 814
Main Authors Salehi Shayegan, Amir Hossein, Zakeri, Ali
Format Journal Article
LanguageEnglish
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
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Summary: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 initial data. In addition, in order to approximate the quasi solution, the finite element method is used. Since the obtained system of linear equations is ill-posed, we apply TSVD regularization. Finally, three numerical examples are given. Numerical results reveal the efficiency and applicability of the proposed method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0928-0219
1569-3945
DOI:10.1515/jiip-2018-0042