Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations
Abstract Consider the simultaneous identification of the initial field and spatial heat source for heat conduction process from extra measurements with the two additional measurement data at different times. The uniqueness and conditional stability for this inverse problem are established by using t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2344-5 |
| _version_ | 1828403184881631232 |
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| author | Bingxian Wang Bin Yang Mei Xu |
| author_facet | Bingxian Wang Bin Yang Mei Xu |
| author_sort | Bingxian Wang |
| collection | DOAJ |
| description | Abstract Consider the simultaneous identification of the initial field and spatial heat source for heat conduction process from extra measurements with the two additional measurement data at different times. The uniqueness and conditional stability for this inverse problem are established by using the properties of a parabolic equation and the representation of solution after reforming the equation. By combining the least squares method with the regularization technique, the inverse problem is transformed into an optimal control problem. Based on the existence and uniqueness of the minimizer of the cost functional, an alternative iteration process is built to solve this optimizing problem by the variational adjoint method. The negative gradient direction is selected as the first search direction. For further iterations, the alternative iteration algorithm is used for the initial field and heat source identification. The efficiency of the proposed scheme is tested by the numerical simulation experiments. |
| first_indexed | 2024-12-10T10:14:48Z |
| format | Article |
| id | doaj.art-4151acbcbc0a4125aee2f41a9c2871e3 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T10:14:48Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4151acbcbc0a4125aee2f41a9c2871e32022-12-22T01:53:02ZengSpringerOpenAdvances in Difference Equations1687-18472019-09-012019111610.1186/s13662-019-2344-5Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizationsBingxian Wang0Bin Yang1Mei Xu2School of Mathematics Science, Huaiyin Normal UniversitySchool of Mathematics Science, Huaiyin Normal UniversitySchool of Mathematics Science, Huaiyin Normal UniversityAbstract Consider the simultaneous identification of the initial field and spatial heat source for heat conduction process from extra measurements with the two additional measurement data at different times. The uniqueness and conditional stability for this inverse problem are established by using the properties of a parabolic equation and the representation of solution after reforming the equation. By combining the least squares method with the regularization technique, the inverse problem is transformed into an optimal control problem. Based on the existence and uniqueness of the minimizer of the cost functional, an alternative iteration process is built to solve this optimizing problem by the variational adjoint method. The negative gradient direction is selected as the first search direction. For further iterations, the alternative iteration algorithm is used for the initial field and heat source identification. The efficiency of the proposed scheme is tested by the numerical simulation experiments.http://link.springer.com/article/10.1186/s13662-019-2344-5Inverse problemParabolic equationInitial fieldHeat sourceAdjoint variational methodNumerics |
| spellingShingle | Bingxian Wang Bin Yang Mei Xu Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations Advances in Difference Equations Inverse problem Parabolic equation Initial field Heat source Adjoint variational method Numerics |
| title | Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations |
| title_full | Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations |
| title_fullStr | Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations |
| title_full_unstemmed | Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations |
| title_short | Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations |
| title_sort | simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations |
| topic | Inverse problem Parabolic equation Initial field Heat source Adjoint variational method Numerics |
| url | http://link.springer.com/article/10.1186/s13662-019-2344-5 |
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