提高多层介质中声学和弹性反源问题的稳定性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Tianjiao Wang, Xiang Xu, Yue Zhao
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引用次数: 0

摘要

本文研究了多层介质中亥姆霍兹方程和纳维方程的反源问题,分别考虑了二维和三维情况。研究表明,每种情况下的稳定性都在不断提高,其特点是有两个主要项:一个是与数据差异相关的霍尔德项,另一个是对数项,随着考虑的频率越多,对数项越小。在二维情况下,对界面和远场数据的测量至关重要。通过采用自由空间的基本解作为测试函数,并利用解的渐近行为和延续原理,可以得到稳定的结果。在三维情况下,需要对界面和人工边界进行测量,并通过应用均质介质中反源问题的论证得出稳定性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Increasing stability of the acoustic and elastic inverse source problems in multi-layered media
This paper investigates inverse source problems for the Helmholtz and Navier equations in multi-layered media, considering both two and three-dimensional cases respectively. The study reveals a consistent increase in stability for each scenario, characterized by two main terms: a Hölder-type term associated with data discrepancy, and a logarithmic-type term that diminishes as more frequencies are considered. In the two-dimensional case, measurements on interfaces and far-field data are essential. By employing the fundamental solution in free-space as the test function and utilizing the asymptotic behavior of the solution and continuation principle, stability results are obtained. In the three-dimensional case, measurements on interfaces and artificial boundaries are taken, and the stability result can be derived by applying the arguments for inverse source problems in homogeneous media.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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