一维时间依赖介质中的散射
1D Scattering through time dependent media with memory
AI总结：
本文提出了一种描述时间依赖介质中波方程解的散射矩阵，并给出了数值求解方法。
摘要：
我们构造了一个具有算子值条目的散射矩阵，用于描述在介电常数具有记忆性且依赖于时间和空间的1+1波方程的解。这类似于描述空间局域扰动的散射矩阵，其中条目是频率的函数，并以傅里叶乘数形式出现在波方程的解中。这为最近Horsley等人论文中的数值构造提供了数学解释。附录由Zhen Huang和Maciej Zworski编写，提出了用于解决本文中考虑的波方程的数值方案。
英文摘要：
We construct a scattering matrix with operator valued entries describing solutions to the 1+1 wave equation where permittivities has memory and depends on time and space. It is the analogue of the scattering matrix for spatially localised perturbations where the entries are functions of frequency and appear as Fourier multipliers in solutions of the wave equation. This provides a mathematical explanation of the numerical construction in the recent paper by Horsley et al. The appendix by Zhen Huang and Maciej Zworski presents a numerical scheme for solving the wave equation considered in this article.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
