A1 Journal article (refereed)
The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability (2022)

Kow, P.-Z., Lin, Y.-H., & Wang, J.-N. (2022). The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability. SIAM Journal on Mathematical Analysis, 54(3), 3379-3419. https://doi.org/10.1137/21M1444941

JYU authors or editors

Publication details

All authors or editorsKow, Pu-Zhao; Lin, Yi-Hsuan; Wang, Jenn-Nan

Journal or seriesSIAM Journal on Mathematical Analysis



Publication year2022


Issue number3

Pages range3379-3419

PublisherSociety for Industrial & Applied Mathematics (SIAM)

Publication countryUnited States

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/85312

Web address of parallel published publication (pre-print)https://arxiv.org/abs/2105.11324


We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative unique continuation properties for the fractional Laplacian. For the stability, we also prove that the log type stability estimate is optimal. The log type estimate shows the striking difference between the inverse problems for the fractional and classical wave equations in the stability issue. The results hold for any spatial dimension n∈N

Keywordspartial differential equationsinverse problems

Free keywordsCalder´on problem; peridynamic; fractional Laplacian; nonlocal; fractional wave equation; strong uniqueness; Runge approximation; logarithmic stability

Contributing organizations

Ministry reportingYes

Reporting Year2022

JUFO rating2

Last updated on 2024-15-06 at 22:25