EXISTENCE, UNIQUENESS AND REGULARITY FOR SOLUTIONSV OF THE CONICAL DIFFRACTION PROBLEM
EXISTENCE, UNIQUENESS AND REGULARITY FOR SOLUTIONSV OF THE CONICAL DIFFRACTION PROBLEM
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DOI：
10.1142/s0218202500000197
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发表时间：
2000-04
影响因子：
3.5
通讯作者：
J. Elschner;Rainer Hinder;G. Schmidt;F. Penzel
中科院分区：
文献类型：
--
作者：
J. Elschner;Rainer Hinder;G. Schmidt;F. Penzel
本文研究了在分段光滑界面上通过准周期传输条件耦合的两个Helmholtz方程。该系统的解在一个方向上是拟周期的，在另一个方向上满足出射波条件。它表明，麦克斯韦方程的时间谐波斜入射平面波的周期性界面的衍射可以减少到这类问题。分析是基于一个强椭圆变分公式的微分问题在一个有界周期细胞涉及非局部边界算子。我们得到了局部有限能量电磁场解的存在唯一性结果。特别注意的是支付的正则性和领先的渐近解的边缘附近的接口。
This paper is devoted to the analysis of two Helmholtz equations in ℝ2 coupled via quasiperiodic transmission conditions on a set of piecewise smooth interfaces. The solution of this system is quasiperiodic in one direction and satisfies outgoing wave conditions with respect to the other direction. It is shown that Maxwell's equations for the diffraction of a time-harmonic oblique incident plane wave by periodic interfaces can be reduced to problems of this kind. The analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for solutions corresponding to electromagnetic fields with locally finite energy. Special attention is paid to the regularity and leading asymptotics of solutions near the edges of the interface.