Identifying the space source term problem for time-space-fractional diffusion equation
Abstract In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02998-y |
| _version_ | 1819228091035156480 |
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| author | Erdal Karapinar Devendra Kumar Rathinasamy Sakthivel Nguyen Hoang Luc N. H. Can |
| author_facet | Erdal Karapinar Devendra Kumar Rathinasamy Sakthivel Nguyen Hoang Luc N. H. Can |
| author_sort | Erdal Karapinar |
| collection | DOAJ |
| description | Abstract In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well. |
| first_indexed | 2024-12-23T10:51:46Z |
| format | Article |
| id | doaj.art-eccbe2e0ef5a40729894332496fbfb08 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T10:51:46Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-eccbe2e0ef5a40729894332496fbfb082022-12-21T17:49:53ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020112310.1186/s13662-020-02998-yIdentifying the space source term problem for time-space-fractional diffusion equationErdal Karapinar0Devendra Kumar1Rathinasamy Sakthivel2Nguyen Hoang Luc3N. H. Can4Department of Mathematics, Çankaya UniversityDepartment of Mathematics, University of RajasthanDepartment of Applied Mathematics, Bharathiar UniversityInstitute of Research and Development, Duy Tan UniversityApplied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang UniversityAbstract In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.http://link.springer.com/article/10.1186/s13662-020-02998-yInverse source problemTime-space-fractional diffusion equationIll-posed problemConvergence estimatesRegularization method |
| spellingShingle | Erdal Karapinar Devendra Kumar Rathinasamy Sakthivel Nguyen Hoang Luc N. H. Can Identifying the space source term problem for time-space-fractional diffusion equation Advances in Difference Equations Inverse source problem Time-space-fractional diffusion equation Ill-posed problem Convergence estimates Regularization method |
| title | Identifying the space source term problem for time-space-fractional diffusion equation |
| title_full | Identifying the space source term problem for time-space-fractional diffusion equation |
| title_fullStr | Identifying the space source term problem for time-space-fractional diffusion equation |
| title_full_unstemmed | Identifying the space source term problem for time-space-fractional diffusion equation |
| title_short | Identifying the space source term problem for time-space-fractional diffusion equation |
| title_sort | identifying the space source term problem for time space fractional diffusion equation |
| topic | Inverse source problem Time-space-fractional diffusion equation Ill-posed problem Convergence estimates Regularization method |
| url | http://link.springer.com/article/10.1186/s13662-020-02998-y |
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