Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements
We consider an inverse problem for simultaneously determining the space-dependent source and the initial distribution in heat conduction equation. First, we study the ill-posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and o...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/8247584 |
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| _version_ | 1832560964066607104 |
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| author | Shufang Qiu Wen Zhang Jianmei Peng |
| author_facet | Shufang Qiu Wen Zhang Jianmei Peng |
| author_sort | Shufang Qiu |
| collection | DOAJ |
| description | We consider an inverse problem for simultaneously determining the space-dependent source and the initial distribution in heat conduction equation. First, we study the ill-posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and obtain the regularization solutions with their stability and convergence results. Furthermore, convergence rates of the regularized solutions are presented under a prior and a posteriori strategies for selecting regularization parameters. Results of numerical examples show that the proposed regularization method is stable and effective for the considered inverse problem. |
| format | Article |
| id | doaj-art-b2bb2c2f3b044f2195bab15ff080aaf8 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-b2bb2c2f3b044f2195bab15ff080aaf82025-02-03T01:26:23ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/82475848247584Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given MeasurementsShufang Qiu0Wen Zhang1Jianmei Peng2School of Science, East China University of Technology, Nanchang, Jiangxi 330013, ChinaSchool of Science, East China University of Technology, Nanchang, Jiangxi 330013, ChinaSchool of Science, East China University of Technology, Nanchang, Jiangxi 330013, ChinaWe consider an inverse problem for simultaneously determining the space-dependent source and the initial distribution in heat conduction equation. First, we study the ill-posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and obtain the regularization solutions with their stability and convergence results. Furthermore, convergence rates of the regularized solutions are presented under a prior and a posteriori strategies for selecting regularization parameters. Results of numerical examples show that the proposed regularization method is stable and effective for the considered inverse problem.http://dx.doi.org/10.1155/2018/8247584 |
| spellingShingle | Shufang Qiu Wen Zhang Jianmei Peng Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements Advances in Mathematical Physics |
| title | Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements |
| title_full | Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements |
| title_fullStr | Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements |
| title_full_unstemmed | Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements |
| title_short | Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements |
| title_sort | simultaneous determination of the space dependent source and the initial distribution in a heat equation by regularizing fourier coefficients of the given measurements |
| url | http://dx.doi.org/10.1155/2018/8247584 |
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