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：2020年11月4日 10:20-11:00

报告地点：数统院307学术报告厅

报告摘要：

This talk is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a rough potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian random field with the covariance operator being described by a classical pseudo-differential operator. The goal is to determine the principal symbol of the covariance operator from the scattered wave measured in a bounded domain which has a positive distance from the domain of the potential. For such a rough potential, the well-posedness of the direct scattering problem in the distribution sense is established by studying an equivalent Lippmann—Schwinger integral equation. For the inverse scattering problem, it is shown with probability one that the principal symbol of the covariance operator can be uniquely determined by the amplitude of the scattered waves averaged over the frequency band from a single realization of the random potential. The analysis employs the Born approximation in high frequency, asymptotics of the Green tensor for the elastic wave equation, and microlocal analysis for the 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 Mathematics with applications, SIAM Journal on Imaging Sciences, SIAM Journal on Mathematical Analysis, Communications in Partial Differential Equations发表论文8篇。