https://scholars.lib.ntu.edu.tw/handle/123456789/626583
標題: | THE CALDERON PROBLEM FOR THE FRACTIONAL WAVE EQUATION: UNIQUENESS AND OPTIMAL STABILITY | 作者: | Kow, PZ Lin, YH JENN-NAN WANG |
關鍵字: | Calderon problem; peridynamic; fractional Laplacian; nonlocal; fractional wave equation; strong uniqueness; Runge approximation; logarithmic stability; MONOTONICITY-BASED INVERSION; EXPONENTIAL INSTABILITY; CONTINUATION; POTENTIALS | 公開日期: | 2022 | 出版社: | SIAM PUBLICATIONS | 卷: | 54 | 期: | 3 | 起(迄)頁: | 3379 | 來源出版物: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 摘要: | 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. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/626583 | ISSN: | 0036-1410 | DOI: | 10.1137/21M1444941 |
顯示於: | 應用數學科學研究所 |
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