Uniqueness and increasing stability in electromagnetic inverse source problems
Uniqueness and increasing stability in electromagnetic inverse source problems
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DOI：
10.1016/j.jde.2021.02.035
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
V. Isakov;Jenn-Nan Wang
中科院分区：
文献类型：
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作者：
V. Isakov;Jenn-Nan Wang
本文从多个波数的边界数据出发，研究了均匀和非均匀介质中电磁波反问题解的唯一性和渐近稳定性。对于源的唯一确定，我们考虑非均匀介质，并在参考域的边界处使用电场和磁场的切向分量。证明依赖于关于波数的傅里叶变换和唯一延拓定理。为了研究源识别的稳定性，我们考虑均匀介质，并测量参考域边界处的吸收数据或电场的切向分量作为附加数据。利用关于波数的傅里叶变换、解析延拓的显式界、惠更斯原理和初边值问题的界，得到了增加(波数间隔较大)的稳定性估计。
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.