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Article Dans Une Revue Mathematische Annalen Année : 2021

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

Résumé

This article is concerned with an inverse problem on simultaneously determining some unknown coefficients and/or an order of derivative in a multidimensional time-fractional 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 -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.
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Dates et versions

hal-03123204 , version 1 (16-01-2024)

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Yavar Kian, Zhiyuan Li, Yikan Liu, Masahiro Yamamoto. The uniqueness of inverse problems for a fractional equation with a single measurement. Mathematische Annalen, 2021, 380 (3-4), pp.1465-1495. ⟨10.1007/s00208-020-02027-z⟩. ⟨hal-03123204⟩
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