各向同性的麦克斯韦方程的内部传输问题及反射参数的估计

数学物理学报 ›› 2013, Vol. 33 ›› Issue (6): 1178-1188.

各向同性的麦克斯韦方程的内部传输问题及反射参数的估计

曲风龙|李希亮

烟台大学数学与信息科学学院山东烟台 264005；山东工商学院数学与信息科学学院山东烟台 264005

收稿日期:2012-03-18 修回日期:2013-01-15 出版日期:2013-12-25 发布日期:2013-12-25
基金资助:
国家自然科学基金(11201402, 11201266)和天元基金(11026098, 11026150)资助

The Interior Transmission Problem for Isotropic Maxwell Equations and Some Estimates on the Index of Refraction

QU Feng-Long, LI Xi-Liang

School of Mathematics and Informational Science, Yantai University, Shandong Yantai 264005； College of Mathematics and Information Sciences, Shandong Institute of Business and Technology, Shandong |Yantai |264005

Received:2012-03-18 Revised:2013-01-15 Online:2013-12-25 Published:2013-12-25
Supported by:
国家自然科学基金(11201402, 11201266)和天元基金(11026098, 11026150)资助

摘要/Abstract

摘要：

考虑时谐电磁波被一个可穿透的、表层覆盖一层很薄的具有高传导性材料的有界物体散射的问题. 该可穿透物体的散射问题可产生内部传输问题. 利用变分方法证明了内部传输问题解的适定性, 将文献[1]的结论推广到传导介质的散射问题中. 在物体的形状以及位置都已经确定的前提下, 进一步利用传输特征值、散射物体的直径及对应于双旋度算子的麦克斯韦第一特征值得到了反射指数的相关估计, 从而推广了文献[2]的结果.

关键词: 适定性;麦克斯韦方程, 传输特征值, 反射参数

Abstract:

We consider the scattering of time-harmonic electromagnetic waves by a bounded, penetrable, inhomogeneous,
isotropic obstacle covered with a thin layer of high conductivity. Such penetrable obstacle problems lead to the so called interior transmission problem. By using a variational argument, the well-posedness of the corresponding interior transmission problem is established, which extends the results of [1] to the conductive boundary value problem case. Under the assumption that the shape and location of the scatter has been determined, we proceed with some estimates on the index of refraction based on the use of the transmission eigenvalues, the radius of the scatter and the first

Maxwell eigenvalue of the curlcurl operator corresponding to the medium, which extends the results in [2].

Key words: Well-posedness, Maxwell equations, Interior transmission problem, Transmission eigenvalues, Index of refraction

中图分类号:

35P25

曲风龙, 李希亮. 各向同性的麦克斯韦方程的内部传输问题及反射参数的估计[J]. 数学物理学报, 2013, 33(6): 1178-1188.

QU Feng-Long, LI Xi-Liang. The Interior Transmission Problem for Isotropic Maxwell Equations and Some Estimates on the Index of Refraction[J]. Acta mathematica scientia,Series A, 2013, 33(6): 1178-1188.

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