Uniqueness and increasing stability in electromagnetic inverse source problems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:283

Article

Isakov, Victor¹  Wang, Jenn-Nan² 

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

[2] Natl Taiwan Univ, Inst Appl Math Sci, Taipei 106, Taiwan

关键词: Electromagnetic waves;    Inverse source problem;    Increasing stability;   

DOI  :  10.1016/j.jde.2021.02.035

来源: Elsevier

【 摘 要 】

In this paper we study the uniqueness and the increasing stability in the inverse source problem for electromagnetic waves in homogeneous and inhomogeneous media from boundary data at multiple wave numbers. For the unique determination of sources, we consider inhomogeneous media and use tangential components of the electric field and magnetic field at the boundary of the reference domain. The proof relies on the Fourier transform with respect to the wave numbers and the unique continuation theorems. To study the increasing stability in the source identification, we consider homogeneous media and measure the absorbing data or the tangential component of the electric field at the boundary of the reference domain as additional data. By using the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, Huygens' principle and bounds for initial boundary value problems, increasing (with larger wave numbers intervals) stability estimate is obtained. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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