瞬时时间镜和具有时间奇异系数的wave equations
Instantaneous time mirrors and wave equations with time-singular coefficients
摘要：
在这项工作中，我们研究的概念，最近在物理学文献中介绍的瞬时时间镜。瞬时时间镜提供了一种新的时间反演方法，与经典技术相比，具有简化的实验装置。在数学层面上，瞬时时间镜是由波动方程系数中时间变量的奇点来模拟的，这种奇点的原型是狄拉克δ。在这项工作中，我们的主要目标是获得重新聚焦的波场，量化的时间反演的质量估计。这相当于分析具有Dirac-type奇性的波动方程并发展适当的正则性理论并推导出统一的估计。
英文摘要：
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.
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。
