Increasing stability in the inverse source problem with many frequencies

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Cheng, Jin¹  Isakov, Victor²  Lu, Shuai¹ 

[1] Fudan Univ, Sch Math Sci, 220 Rd Handan, Shanghai 200433, Peoples R China

[2] Wichita State Univ, Dept Math Stat & Phys, Wichita, KS 67260 USA

关键词: Increasing stability;    Inverse source problems;    Multiple frequencies;   

DOI  :  10.1016/j.jde.2015.11.030

来源: Elsevier

【 摘 要 】

We study increasing stability in the interior inverse source problem for the Helmholtz equation from boundary Cauchy data for multiple wave numbers. By using the Fourier transform with respect to the wave number, explicit bounds for the analytic continuation, uniqueness of the continuation results, and exact observability bounds for the wave equation, a sharp uniqueness result and an increasing (with larger wave numbers intervals) stability estimate are obtained. Numerical examples in 3 spatial dimension support the theoretical prediction. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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