发表机构
Karlsruhe Institute of Technology; Univ. Polytechnique Hauts-de-France; INSA Hauts-de-France（卡尔斯鲁厄理工学院; 上法兰西工业大学; 上法兰西国立应用科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究平面界面阻尼下线性麦克斯韦方程组的适定性、正则性与稳定性，证明压缩半群与隐藏正则性，并分解动力学为酉部分与强稳定部分，在非折射非共振情形用矩条件刻画衰减初始场。
AI 中文摘要
我们研究一个长方体上的线性麦克斯韦方程组，该长方体被一个平面界面分成两部分，穿过该界面时，切向磁场与切向电场成比例地跳跃。这类条件出现在原子级薄超材料的建模中，其中薄片被有效的表面电流所替代。在允许界面上存在表面电荷的状态空间中，我们证明了该问题由一个压缩半群支配。为此，我们提供了底层函数空间的稠密性结果、Weber型不等式和迹估计。我们进一步证明了一个隐藏的正则性结果，指出麦克斯韦算子定义域中的场是分片一阶Sobolev正则的。由于阻尼仅作用于界面，能量并非对所有初始场都衰减。我们将动力学分解为一个酉部分（由对阻尼不可见的特征模态承载）和一个强稳定部分。在非折射情形且界面位置非共振的情况下，我们通过两个矩条件刻画了衰减的初始场。
英文摘要
We study linear Maxwell's equations on a cuboid that is split into two parts by a planar interface, across which the tangential magnetic field jumps proportionally to the tangential electric field. Conditions of this type arise in the modeling of atomically thin metamaterials, where the sheet is replaced by an effective surface current. Working in a state space that admits a surface charge on the interface, we show that the problem is governed by a contraction semigroup. To this end, we provide density results, Weber-type inequalities, and trace estimates for the underlying function spaces. We further prove a hidden regularity result, stating that the fields in the domain of the Maxwell operator are piecewise Sobolev regular of first order. Since the damping acts on the interface only, the energy does not decay for all initial fields. We decompose the dynamics into a unitary part, carried by the eigenmodes that are invisible to the damping, and a strongly stable part. In the non-refracting case with a non-resonant interface position, we characterize the decaying initial fields by two moment conditions.
Comments32 pages, 1 figure
