Stability for the multifrequency inverse medium problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Bao, Gang¹  Triki, Faouzi² 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Univ Grenoble Alpes, CNRS, UMR 5224, Lab Jean Kuntzmann, 700 Ave Centrale, F-38401 St Martin Dheres, France

关键词: Inverse medium problem;    Helmholtz equation;    Stability estimates;    Trace formula;    Scattering resonances;   

DOI  :  10.1016/j.jde.2020.05.021

来源: Elsevier

【 摘 要 】

The solution of a multi -frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived when the frequency takes value in a bounded interval. It is showed that the ill-posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger. More precisely, under certain regularity assumptions on the refractive index, the estimates indicate that the power in Holder stability is an increasing function of the largest value in the frequency band. Finally, a Lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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