离散赫尔姆霍兹方程的反源问题

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-08-28 DOI:10.1088/1361-6420/ad7054

Roman Novikov, Basant Lal Sharma

引用次数: 0

摘要

我们考虑的是方阵 Zd, d⩾1 上离散亥姆霍兹算子的多频反源问题。我们考虑了有相位信息和无相位信息的情况。我们证明了该问题在紧凑支撑源函数情况下的唯一性结果，并举例说明了其非唯一性，同时建立了相位情况下的李普希兹稳定性估计。我们还提供了与玻恩近似离散薛定谔算子反散射问题的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Inverse source problem for discrete Helmholtz equation

We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice

d⩾1

. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided.

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来源期刊

Inverse Problems 数学-物理：数学物理

CiteScore

4.40

自引率

14.30%

发文量

115

审稿时长

2.3 months

期刊介绍： An interdisciplinary journal combining mathematical and experimental papers on inverse problems with theoretical, numerical and practical approaches to their solution. As well as applied mathematicians, physical scientists and engineers, the readership includes those working in geophysics, radar, optics, biology, acoustics, communication theory, signal processing and imaging, among others. The emphasis is on publishing original contributions to methods of solving mathematical, physical and applied problems. To be publishable in this journal, papers must meet the highest standards of scientific quality, contain significant and original new science and should present substantial advancement in the field. Due to the broad scope of the journal, we require that authors provide sufficient introductory material to appeal to the wide readership and that articles which are not explicitly applied include a discussion of possible applications.