论文标题
瞬时时间镜和波动方程，带有时间呈线系数
Instantaneous time mirrors and wave equations with time-singular coefficients
论文作者
论文摘要
我们在这项工作中研究了物理文献最近引入的瞬时时间反射镜的概念。与经典技术相比，瞬时时间镜使用简化的实验设置提供了一种新的时间逆转方法。在数学层面上，瞬时时间镜在波动方程的系数中以时间变量的奇异性建模，而这种奇异性的原型是DIRAC DELTA。我们在这项工作中的主要目标是对量化时间逆转质量的波场进行重新关注的估计。这相当于用dirac型奇点分析波方程，并发展出适当的规律性理论并得出统一的估计。
We study in this work the concept of instantaneous time mirrors that were recently introduced in the physics literature. Instantaneous time mirrors offer a new method for time reversal with a simplified experimental setup compared to classical techniques. At the mathematical level, instantaneous time mirrors are modeled by singularities in the time variable in the coefficients of a wave equation, and a prototype of such singularity is a Dirac delta. Our main goal in this work is to obtain refocusing estimates for the wavefield that quantify the quality of time reversal. This amounts to analyze the wave equation with Dirac-type singularities and develop a proper regularity theory as well as derive uniform estimates.
