Inverse Source Problem for Sobolev Equation with Fractional Laplacian
In this paper, we are interested in the problem of determining the source function for the Sobolev equation with fractional Laplacian. This problem is ill-posed in the sense of Hadamard. In order to edit the instability instability of the solution, we applied the fractional Landweber method. In the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/1035118 |
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| _version_ | 1832565808273817600 |
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| author | Nguyen Duc Phuong Van Tien Nguyen Le Dinh Long |
| author_facet | Nguyen Duc Phuong Van Tien Nguyen Le Dinh Long |
| author_sort | Nguyen Duc Phuong |
| collection | DOAJ |
| description | In this paper, we are interested in the problem of determining the source function for the Sobolev equation with fractional Laplacian. This problem is ill-posed in the sense of Hadamard. In order to edit the instability instability of the solution, we applied the fractional Landweber method. In the theoretical analysis results, we show the error estimate between the exact solution and the regularized solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Finally, we investigate the convergence of the source function when fractional order β⟶1+. |
| format | Article |
| id | doaj-art-ac392b0075cf46b0a66fbb09e329bfd2 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ac392b0075cf46b0a66fbb09e329bfd22025-02-03T01:06:38ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/1035118Inverse Source Problem for Sobolev Equation with Fractional LaplacianNguyen Duc Phuong0Van Tien Nguyen1Le Dinh Long2Industrial University of Ho Chi Minh CityFaculty of MathDivision of Applied MathematicsIn this paper, we are interested in the problem of determining the source function for the Sobolev equation with fractional Laplacian. This problem is ill-posed in the sense of Hadamard. In order to edit the instability instability of the solution, we applied the fractional Landweber method. In the theoretical analysis results, we show the error estimate between the exact solution and the regularized solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Finally, we investigate the convergence of the source function when fractional order β⟶1+.http://dx.doi.org/10.1155/2022/1035118 |
| spellingShingle | Nguyen Duc Phuong Van Tien Nguyen Le Dinh Long Inverse Source Problem for Sobolev Equation with Fractional Laplacian Journal of Function Spaces |
| title | Inverse Source Problem for Sobolev Equation with Fractional Laplacian |
| title_full | Inverse Source Problem for Sobolev Equation with Fractional Laplacian |
| title_fullStr | Inverse Source Problem for Sobolev Equation with Fractional Laplacian |
| title_full_unstemmed | Inverse Source Problem for Sobolev Equation with Fractional Laplacian |
| title_short | Inverse Source Problem for Sobolev Equation with Fractional Laplacian |
| title_sort | inverse source problem for sobolev equation with fractional laplacian |
| url | http://dx.doi.org/10.1155/2022/1035118 |
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