THE CALDERON PROBLEM FOR THE FRACTIONAL WAVE EQUATION: UNIQUENESS AND OPTIMAL STABILITY
Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Journal Volume
54
Journal Issue
3
Pages
3379
Date Issued
2022
Author(s)
Abstract
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.
Subjects
Calderon problem; peridynamic; fractional Laplacian; nonlocal; fractional wave equation; strong uniqueness; Runge approximation; logarithmic stability; MONOTONICITY-BASED INVERSION; EXPONENTIAL INSTABILITY; CONTINUATION; POTENTIALS
SDGs
Publisher
SIAM PUBLICATIONS
Type
journal article