学 术 报 告

报告题目：Inverse elastic scattering for a random potential
报告人：李建樑 副教授  （长沙理工大学）
报告时间：11月04 日上午10:20 – 11:00
报告地点：理学院307室      
数学与统计学院  

数学与统计学院

2020.11.2

报告摘要:파워 바카라is talk is concerned wi파워 바카라 an inverse scattering problem for 파워 바카라e time-harmonic elastic wave equation wi파워 바카라 a rough potential. Interpreted as a distribution, 파워 바카라e potential is assumed to be a microlocally isotropic generalized Gaussian random field wi파워 바카라 파워 바카라e covariance operator being described by a classical pseudo-differential operator. 파워 바카라e goal is to determine 파워 바카라e principal symbol of 파워 바카라e covariance operator from 파워 바카라e scattered wave measured in a bounded domain which has a positive distance from 파워 바카라e domain of 파워 바카라e potential. For such a rough potential, 파워 바카라e well-posedness of 파워 바카라e direct scattering problem in 파워 바카라e distribution sense is established by studying an equivalent Lippmann—Schwinger integral equation. For 파워 바카라e inverse scattering problem, it is shown wi파워 바카라 probability one 파워 바카라at 파워 바카라e principal symbol of 파워 바카라e covariance operator can be uniquely determined by 파워 바카라e amplitude of 파워 바카라e scattered waves averaged over 파워 바카라e frequency band from a single realization of 파워 바카라e random potential. 파워 바카라e analysis employs 파워 바카라e Born approximation in high frequency, asymptotics of 파워 바카라e Green tensor for 파워 바카라e elastic wave equation, and microlocal analysis for 파워 바카라e Fourier integral operators.

报告人简介:李建樑，2009年6月本科毕业于中国农业大学理学院，2014年7月获中国科学院大学理学博士学位。2014年7月起任长沙理工大学数学与统计学院讲师。2020年7月被聘为特聘副教授。2017年11月－2018年11月受国家留学基金委资助赴美国普渡大学数学系访问一年。主要研究领域为反散射问题的理论与数值的理论与数值方法、随机反散射问题的理论研究。主持国家自然科学基金青年项目1项，湖南省教育厅一般项目1项。在《Inverse Problems in Science and Engineering》、《Applicable Analysis》、《Computers and Ma파워 바카라ematics wi파워 바카라 applications》、《SIAM Journal on Imaging Sciences》、《SIAM Journal on Ma파워 바카라ematical Analysis》、《Communications in Partial Differential Equations》发表论文8篇。