Simultaneous determination of source term and the initial value in the space-fractional diffusion problem by a novel modified quasi-reversibility regularization method
Abstract This paper deals with an inverse problem of determining source term and initial data simultaneously for a space-fractional diffusion equation in a strip domain, with the aid of extra measurement data at a fixed time. The uniqueness results are obtained by a simple trick based on the linear...
Saved in:
| Published in: | Physica scripta 2023-02, Vol.98 (2), p.25201 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Abstract This paper deals with an inverse problem of determining source term and initial data simultaneously for a space-fractional diffusion equation in a strip domain, with the aid of extra measurement data at a fixed time. The uniqueness results are obtained by a simple trick based on the linear property of the proposed equation. Since this problem is ill-posed, a modified quasi-reversibility method is obtained by employing the Fourier transform. Error estimates for source term and initial value are obtained from a suitable parameter choice rule. Finally, several numerical examples show that the proposed regularization method is effective and stable. |
|---|---|
| ISSN: | 0031-8949 1402-4896 |