时谐双谐波方程反腔散射问题的唯一性

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-04-25 DOI:10.1088/1361-6420/ad438c

Heping Dong, Peijun Li

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引用次数: 0

摘要

本文探讨了与二维时谐双谐波方程相关的反向空腔散射问题。其目的是确定空腔的域或形状。本文证明了边界值问题解的格林表示法，并确认了双谐波的亥姆霍兹分量与所产生的远场模式之间的一一对应关系。推导出两种混合互易关系，将平面波产生的散射场与各类点源产生的远场模式联系起来。此外，我们还探讨了点源产生的散射场的对称关系。最后，我们利用远场模式和无相位近场数据，给出了逆问题的两个唯一性结果。

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Uniqueness of an inverse cavity scattering problem for the time-harmonic biharmonic wave equation

This paper addresses an inverse cavity scattering problem associated with the time-harmonic biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the solution to the boundary value problem, and the one-to-one correspondence is confirmed between the Helmholtz component of biharmonic waves and the resulting far-field patterns. Two mixed reciprocity relations are deduced, linking the scattered field generated by plane waves to the far-field pattern produced by various types of point sources. Furthermore, the symmetry relations are explored for the scattered fields generated by point sources. Finally, we present two uniqueness results for the inverse problem by utilizing both far-field patterns and phaseless near-field data.

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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.