The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain
In this paper, the inverse problem for identifying the initial value of a time fractional nonhomogeneous diffusion equation in a columnar symmetric region is studied. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. The fractional Tikhonov regularization met...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/8/1633 |
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| author | Yong-Gang Chen Fan Yang Xiao-Xiao Li Dun-Gang Li |
| author_facet | Yong-Gang Chen Fan Yang Xiao-Xiao Li Dun-Gang Li |
| author_sort | Yong-Gang Chen |
| collection | DOAJ |
| description | In this paper, the inverse problem for identifying the initial value of a time fractional nonhomogeneous diffusion equation in a columnar symmetric region is studied. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. The fractional Tikhonov regularization method is applied to solve this problem and obtain the regularization solution. The error estimations between the regularization solution and the exact solution are also obtained under the priori and the posteriori regularization parameter choice rules, respectively. Some examples are given to show this method’s effectiveness. |
| first_indexed | 2024-03-09T03:46:38Z |
| format | Article |
| id | doaj.art-a690159cdf0641a08778cf759a880cb6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:46:38Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a690159cdf0641a08778cf759a880cb62023-12-03T14:33:18ZengMDPI AGSymmetry2073-89942022-08-01148163310.3390/sym14081633The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical DomainYong-Gang Chen0Fan Yang1Xiao-Xiao Li2Dun-Gang Li3School of Science, China University of Petroleum, Qindao 266580, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou 730050, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou 730050, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou 730050, ChinaIn this paper, the inverse problem for identifying the initial value of a time fractional nonhomogeneous diffusion equation in a columnar symmetric region is studied. This is an ill-posed problem, i.e., the solution does not depend continuously on the data. The fractional Tikhonov regularization method is applied to solve this problem and obtain the regularization solution. The error estimations between the regularization solution and the exact solution are also obtained under the priori and the posteriori regularization parameter choice rules, respectively. Some examples are given to show this method’s effectiveness.https://www.mdpi.com/2073-8994/14/8/1633time-fractional nonhomogeneous diffusion equationcolumnar symmetric domainill-posed problemfractional Tikhonov method |
| spellingShingle | Yong-Gang Chen Fan Yang Xiao-Xiao Li Dun-Gang Li The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain Symmetry time-fractional nonhomogeneous diffusion equation columnar symmetric domain ill-posed problem fractional Tikhonov method |
| title | The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain |
| title_full | The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain |
| title_fullStr | The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain |
| title_full_unstemmed | The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain |
| title_short | The Fractional Tikhonov Regularization Method to Identify the Initial Value of the Nonhomogeneous Time-Fractional Diffusion Equation on a Columnar Symmetrical Domain |
| title_sort | fractional tikhonov regularization method to identify the initial value of the nonhomogeneous time fractional diffusion equation on a columnar symmetrical domain |
| topic | time-fractional nonhomogeneous diffusion equation columnar symmetric domain ill-posed problem fractional Tikhonov method |
| url | https://www.mdpi.com/2073-8994/14/8/1633 |
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