讲座主题：Diffraction by periodic curves of Neumann kind

专家姓名：胡广辉

工作单位：南开大学数学科学学院

讲座时间：2022年11月25日 10:30-11:30

讲座地点：腾讯会议：312-899-144

主办单位：tyc1286太阳集团数学与信息科学学院

内容摘要：

The Rayleigh expansion radiation condition (which was originally proposed by Lord Rayleigh in 1907) has been widely used in the literature concerning the mathematical analysis and numerical approximation of wave scattering in periodic structures. With the Fredholm theory, it is also well known that the forward scattering model is well-posed for all incident frequencies excluding a discrete set with the only accumulating point at infinity. However, the Rayleigh expansion radiation condition does not always lead to uniqueness (although existence can always be justified via variational argument), because of the existence of guided/Floquet wave modes to the homogeneous problem, which exponentially decay in the direction orthogonal to the periodicity direction. In this talk, I will propose a new radiation condition to ensure uniqueness of forward diffraction problem from periodic curves of Neumann kind. This new condition is derived from a singular perturbation argument based on the limiting absorption principle.

主讲人介绍：

胡广辉，现任南开大学数学科学学院科学工程与计算系教授。2009年获中国科学院数学与系统科学研究院博士学位。2009至2016年在德国莱布尼茨协会维尔斯特拉斯研究所做博士后工作，2012至2015年独立主持德国研究协会科研项目。2016年3月份入选国家海外高层次青年人才计划，2016.09-2020.05就工作于北京计算科学研究中心，2020年3月份入选德国洪堡资深学者访问项目。胡广辉博士主要从事波方程的数学理论研究和偏微分方程反问题及其计算方法研究,目前已在ARMA,M3AS,JCP,JDE,JMPA,IP,SIAM系列杂志发表学术论文70余篇。