THE CALDERON PROBLEM FOR THE FRACTIONAL WAVE EQUATION: UNIQUENESS AND OPTIMAL STABILITY

被引：14

作者：

Kow, Pu-Zhao ^{[1
]}

Lin, Yi-Hsuan ^{[2
]}

Wang, Jenn-Nan ^{[3
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, FI-40014 Jyvaskyla, Finland

[2] Natl Yang Ming Chiao Tung Univ, Dept Appl Math, Hsinchu 30050, Taiwan

[3] Natl Taiwan Univ, Inst Appl Math Sci, Taipei 106, Taiwan

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2022年 / 54卷 / 03期

关键词：

Calderon problem; peridynamic; fractional Laplacian; nonlocal; fractional wave equation; strong uniqueness; Runge approximation; logarithmic stability; MONOTONICITY-BASED INVERSION; EXPONENTIAL INSTABILITY; CONTINUATION; POTENTIALS;

D O I：

10.1137/21M1444941

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 is an element of N.

引用

页码：3379 / 3419

页数：41

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