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The uniqueness of inverse problems for a fractional equation with a single measurement

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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
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)

Submitter: 劉 逸侃

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