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Stability for an Inverse Source Problem of the Biharmonic Operator

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-Schrödinger operator Δ2+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 ϕ and their Laplacian Δϕ corresponding to the bi-Schrödinger operator. These types of upper bounds was proved by Hassell and Tao [Math. Res. Lett., 9 (2012), pp. 289--305] for the Schrödinger operator. The meromorphic continuation is investigated for the resolvent of the bi-Schrödinger operator, which is shown to have a resonance-free region and an estimate of L2comp−L2loc 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.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.81 No.6 November-December 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2503-2525

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

STABILITY
INVERSE SOURCE PROBLEM
BIHARMONIC OPERATOR
RESOLVENT ESTIMATE

Info Detail Spesifik

https://doi.org/10.1137/21M1407148

Pernyataan Tanggungjawab

Peijun Li, Xiaohua Yao, Yue Zhao

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