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Inverse moving source problem for time-fractional evolution equations : determination of profiles
| Title: | Inverse moving source problem for time-fractional evolution equations : determination of profiles |
| Authors: | Liu, Yikan Browse this author →KAKEN DB | | Hu, Guanghui Browse this author | | Yamamoto, Masahiro Browse this author →KAKEN DB |
| Keywords: | inverse moving source problem | | time-fractional evolution equation | | vanishing property | | uniqueness |
| Issue Date: | 12-Jul-2021 |
| Publisher: | IOP Publishing |
| Journal Title: | Inverse problems |
| Volume: | 37 |
| Issue: | 8 |
| Start Page: | 084001 |
| Publisher DOI: | 10.1088/1361-6420/ac0c20 |
| Abstract: | This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order alpha is an element of (0, 2] in time. In the first problem, the sources are supposed to move along known straight lines, and we suitably choose partial interior observation data in finite time. Reducing the problems to the determination of initial values, we prove the unique determination of one and two moving source profiles for 0 < alpha <= 1 and 1 < alpha <= 2, respectively. In the second problem, the orbits of moving sources are assumed to be known, and we consider the full lateral Cauchy data. At the cost of infinite observation time, we prove the unique determination of one moving source profile by constructing test functions. |
| Rights: | This is the Accepted Manuscript version of an article accepted for publication in [Inverse Problems]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at [10.1088/1361-6420/ac0c20]. |
| Publisher URI: | https://arxiv.org/abs/2002.00194 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/86491 |
| Appears in Collections: | 電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 劉 逸侃
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