Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-19
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
This paper is devoted to identify a space-dependent source function in a multiterm time-fractional diffusion equation with nonhomogeneous boundary condition from a part of noisy boundary data.
The well-posedness of a weak solution for the corresponding direct problem is proved by the variational method.
We firstly investigate the uniqueness of an inverse initial problem by the analytic continuation technique and the Laplace transformation.
Then, the uniqueness of the inverse source problem is derived by employing the fractional Duhamel principle.
The inverse problem is solved by the Levenberg-Marquardt regularization method, and an approximate source function is found.
Numerical examples are provided to show the effectiveness of the proposed method in one- and two-dimensional cases.
American Psychological Association (APA)
Sun, L. L.& Yan, X. B.. 2020. Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition. Advances in Mathematical Physics،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1127299
Modern Language Association (MLA)
Sun, L. L.& Yan, X. B.. Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition. Advances in Mathematical Physics No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1127299
American Medical Association (AMA)
Sun, L. L.& Yan, X. B.. Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition. Advances in Mathematical Physics. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1127299
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1127299