从内部数据中恢复半线性亥姆霍兹方程组的系数

IF 2 2区数学 Q1 MATHEMATICS, APPLIED

Inverse Problems Pub Date : 2024-03-08 DOI:10.1088/1361-6420/ad2cf9

Kui Ren, Nathan Soedjak

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引用次数: 0

摘要

我们研究了一个半线性亥姆霍兹方程耦合系统的逆问题，我们感兴趣的是根据热声成像等应用中测量到的内部数据重建系统中的多个系数。该系统是异质介质中二次谐波生成过程的简化模型。我们基于一阶和高阶线性化技术，推导出在边界数据较小的情况下反问题的唯一性和稳定性。我们还提供了数值模拟，以说明噪声数据的重构质量。

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Recovering coefficients in a system of semilinear Helmholtz equations from internal data

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. The system serves as a simplified model of the second harmonic generation process in a heterogeneous medium. We derive results on the uniqueness and stability of the inverse problem in the case of small boundary data based on the technique of first- and higher-order linearization. Numerical simulations are provided to illustrate the quality of reconstructions that can be expected from noisy 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.