论文标题
麦克斯韦方程的逆随机源问题
An inverse random source problem for Maxwell's equations
论文作者
论文摘要
本文涉及三维时间谐波麦克斯韦方程的逆随机源问题。源被认为是具有相关组件的中心复合物值高斯矢量场，其协方差操作员是伪分化的操作员。建立了直接源散射问题的适当性，并给出了电磁场的规律性。对于逆源散射问题，证明协方差算子的微相关强度矩阵被证明是由在开放式域中分离的电场的高频期望的高频限制在源源的支持下唯一确定的。特别是，我们表明，强度基质的对角线条目只能通过使用电场的幅度来唯一确定。此外，通过在频率上推论电场的厄尔及态关系，将该结果扩展到几乎可以肯定的感觉。
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its covariance operator is a pseudo-differential operator. The well-posedness of the direct source scattering problem is established and the regularity of the electromagnetic field is given. For the inverse source scattering problem, the micro-correlation strength matrix of the covariance operator is shown to be uniquely determined by the high frequency limit of the expectation of the electric field measured in an open bounded domain disjoint with the support of the source. In particular, we show that the diagonal entries of the strength matrix can be uniquely determined by only using the amplitude of the electric field. Moreover, this result is extended to the almost surely sense by deducing an ergodic relation for the electric field over the frequencies.
