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The uniqueness of inverse problems for a fractional equation with a single measurement
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The uniqueness of inverse problems for a fractional equation with a single measurement
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Journal Article
The uniqueness of inverse problems for a fractional equation with a single measurement
2021
Overview
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
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.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V,Springer Verlag
