Paper Info
Title
STABILITY FOR AN INVERSE SOURCE PROBLEM OF THE BIHARMONIC OPERATOR
Abstract
In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in R3. An eigenvalue problem is considered for the bi-Schro"\dinger operator \Delta 2 + V (x) on a ball which contains the support of the potential V. A Weyl-type law is proved for the upper bounds of spherical normal derivatives of both the eigenfunctions \phi and their Laplacian \Delta \phi corresponding to the bi-Schro"\dinger operator. These types of upper bounds was proved by Hassell and Tao [Math. Res. Lett., 9 (2012), pp. 289305] for the Schro"\dinger operator. The meromorphic continuation is investigated for the resolvent of the bi-Schro"\dinger operator, which is shown to have a resonance-free region and an estimate of L2comp - L2lo c type for the resolvent. As an application, we prove a bound of the analytic continuation of the data with respect to the frequency. Finally, the stability estimate is derived for the inverse source problem. The estimate consists of the Lipschitz-type data discrepancy and the high-frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases.
Year
DOI
Venue
2021
10.1137/21M1407148
SIAM JOURNAL ON APPLIED MATHEMATICS
Keywords
DocType
Volume
resolvent estimate, inverse source problem, biharmonic operator, stability
Journal
81
Issue
ISSN
Citations 
6
0036-1399
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Peijun Li101.35
Xiaohua Yao200.34
Yue Zhao318633.54