论文标题
电磁逆源问题的独特性和稳定性提高
Uniqueness and increasing stability in electromagnetic inverse source problems
论文作者
论文摘要
在本文中，我们研究了来自边界数据以多波数的边界数据中均质和不均匀介质中电磁波的逆源问题的唯一性和稳定性的增加。为了确定来源的独特确定，我们考虑不均匀的介质，并使用参考域边界处的电场和磁场的切向组件。证明依赖于傅立叶变换，相对于波数和唯一的延续定理。为了研究源识别的稳定性的提高，我们考虑均质介质并测量参考域边界处电场的吸收数据或电场的切向组件，作为附加数据。通过使用有关波数的傅立叶变换，分析性延续的显式边界，Huygens的原理和初始边界值问题的边界，增加（随着较大的波数间隔），获得了稳定性估计值。
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.
