open access

https://hdl.handle.net/2115/82210

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

英語

2020-07-09

Springer

Mathematische annalen

380(3-4)

1465-1495

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.

学術雑誌論文

Accepted Manuscript

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

0025-5831