A multi-frequency inverse source problem
A multi-frequency inverse source problem
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DOI：
10.1016/j.jde.2010.08.013
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发表时间：
2010-12
影响因子：
2.4
通讯作者：
G. Bao;Junshan Lin;Faouzi Triki
中科院分区：
文献类型：
--
作者：
G. Bao;Junshan Lin;Faouzi Triki
本文讨论了一个源的反问题，它通过测量多个频率的辐射场来确定源。严格的稳定性估计建立时，背景介质是均匀的。结果表明，反问题的不适定性随着频率的增加而减小。在对源函数的正则性假设下，进一步证明了随着频率的增加，源反问题的对数稳定性转化为线性稳定性。
This paper is concerned with an inverse source problem that determines the source from measurements of the radiated fields away at multiple frequencies. Rigorous stability estimates are established when the background medium is homogeneous. It is shown that the ill-posedness of the inverse problem decreases as the frequency increases. Under some regularity assumptions on the source function, it is further proven that by increasing the frequency, the logarithmic stability converts to a linear one for the inverse source problem.