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The uniqueness of inverse problems for a fractional equation with a single measurement
Title: | The uniqueness of inverse problems for a fractional equation with a single measurement |
Authors: | Kian, Yavar Browse this author | Li, Zhiyuan Browse this author | Liu, Yikan Browse this author →KAKEN DB | Yamamoto, Masahiro Browse this author |
Issue Date: | 9-Jul-2020 |
Publisher: | Springer |
Journal Title: | Mathematische annalen |
Volume: | 380 |
Issue: | 3-4 |
Start Page: | 1465 |
End Page: | 1495 |
Publisher DOI: | 10.1007/s00208-020-02027-z |
Abstract: | This article is concerned with an inverse problem on simultaneously determining some unknown coefficients and/or an order of derivative in a multidimensional timefractional evolution equation either in a Euclidean domain or on a Riemannian manifold. Based on a special choice of the Dirichlet boundary input, we prove the unique recovery of at most two out of four x-dependent coefficients (possibly with an extra unknown fractional order) by a single measurement of the partial Neumann boundary output. Especially, both a vector-valued velocity field of a convection term and a density can also be uniquely determined. The key ingredient turns out to be the time-analyticity of the decomposed solution, which enables the construction of Dirichlet-to-Neumann maps in the frequency domain and thus the application of inverse spectral results. |
Rights: | This is a post-peer-review, pre-copyedit version of an article published in Mathematische Annalen. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00208-020-02027-z |
Type: | article (author version) |
URI: | http://hdl.handle.net/2115/82210 |
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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