A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme
We consider the inverse source problem for heat equation, where the source term has the form f(t)ϕ(x). We give a numerical algorithm to compute unknown source term f(t). Also, we give a stability estimate in the case that f(t) is a piecewise constant function.
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/9504829 |
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| _version_ | 1832561220821975040 |
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| author | Xianzheng Jia |
| author_facet | Xianzheng Jia |
| author_sort | Xianzheng Jia |
| collection | DOAJ |
| description | We consider the inverse source problem for heat equation, where the source term has the form f(t)ϕ(x). We give a numerical algorithm to compute unknown source term f(t). Also, we give a stability estimate in the case that f(t) is a piecewise constant function. |
| format | Article |
| id | doaj-art-65d475aae32d4d8d8f0b401a1b3edeec |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-65d475aae32d4d8d8f0b401a1b3edeec2025-02-03T01:25:41ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/95048299504829A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical SchemeXianzheng Jia0Shandong University of Technology, Shandong 255000, ChinaWe consider the inverse source problem for heat equation, where the source term has the form f(t)ϕ(x). We give a numerical algorithm to compute unknown source term f(t). Also, we give a stability estimate in the case that f(t) is a piecewise constant function.http://dx.doi.org/10.1155/2016/9504829 |
| spellingShingle | Xianzheng Jia A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme Advances in Mathematical Physics |
| title | A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme |
| title_full | A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme |
| title_fullStr | A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme |
| title_full_unstemmed | A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme |
| title_short | A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme |
| title_sort | lipschitz stability estimate for the inverse source problem and the numerical scheme |
| url | http://dx.doi.org/10.1155/2016/9504829 |
| work_keys_str_mv | AT xianzhengjia alipschitzstabilityestimatefortheinversesourceproblemandthenumericalscheme AT xianzhengjia lipschitzstabilityestimatefortheinversesourceproblemandthenumericalscheme |