Uniqueness of refractive indices and transmission coefficients by an inhomogeneous medium in acoustic scattering

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

IMA Journal of Applied Mathematics Pub Date : 2023-09-02 DOI:10.1093/imamat/hxad022

Jianlin Xiang, Guozheng Yan

引用次数: 0

Abstract

We are concerned with the inverse scattering problem of recovering the refractive indices and transmission coefficients by the corresponding acoustic far-field measurement encoded into the scattering amplitude. Our first uniqueness result is to determine a constant refractive index by the fixed incident direction scattering amplitude, the proof of which is mainly based on the discreteness of the corresponding interior transmission eigenvalues. Then motivated by the previous work Xiang & Yan (2021), the second uniqueness result is established to recover a piecewise constant refractive index from the far-field pattern at a fixed frequency.

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非均匀介质声散射中折射率和透射系数的唯一性

本文研究了通过将相应的声远场测量值编码到散射振幅中来恢复折射率和透射系数的反散射问题。我们的第一个唯一性结果是通过固定的入射方向散射振幅来确定一个恒定的折射率，其证明主要基于对应的内部透射特征值的离散性。然后在之前的工作Xiang & Yan(2021)的激励下，建立第二个唯一性结果，从固定频率的远场模式中恢复分段恒定折射率。

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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来源期刊

IMA Journal of Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

24 months

期刊介绍： The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered. The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.