We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method, we reformulate the problem in the Laplace domain using the electric field equation inside the scatterer and a system of boundary integral equations for the scattered electric field in free space. To analyze this nonlocal boundary problem, we replace it by an equivalent boundary value problem. Existence, uniqueness and stability of the weak solution to the equivalent BVP are established in appropriate function spaces in terms of the Laplace transformed variable. The stability bounds are translated into time-domain estimates which determine the regularity of the solution in terms of the regularity of the problem data. These estimates can be easily converted into error estimates for a numerical discretization on the convolution quadrature for time evolution.

翻译：本文研究了当入射电磁波照射嵌入无限空间中的介质散射体或涂层导体时产生的瞬态散射场和透射场。通过应用边界场方程方法，我们利用散射体内部的电场方程和自由空间中散射电场的边界积分方程组，在拉普拉斯域中重新表述该问题。为了分析这一非局部边界问题，我们将其替换为一个等价的边值问题。在拉普拉斯变换变量的相关函数空间中，建立了等价边值问题弱解的存在性、唯一性和稳定性。稳定性界限被转化为时域估计，从而根据问题数据的正则性确定解的正则性。这些估计可以很容易地转化为用于时间演化的卷积求积法数值离散化的误差估计。