李建樑博士学术报告

报告题目：Inverse random source problems for time-harmonic acoustic and elastic waves

报告人: 李建樑 博士（长沙理工大学）

报告时间: 2019.12.26 周四下午4:30-5:30

报告地点: 数学院大会议室341

内容摘要：This talk concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a domain away from the source region. The source is assumed to be a microlocally isotropic generalized Gaussian random function such that its covariance operator is a classical pseudo-differential operator. Given such a distributional source, the direct problem is shown to have a unique solution by using an integral equation approach and the Sobolev embedding theorem. For the inverse problem, we demonstrate that the amplitude of the scattering field averaged over the frequency band, obtained from a single realization of the random source, determines uniquely the principle symbol of the covariance operator. The analysis employs asymptotic expansions of the Green functions and microlocal analysis of the Fourier integral operators associated with the Helmholtz and Navier equations.

报告人简介: 李建樑，中国科学院大学理学博士。2014年7月起任长沙理工大学数学与统计学院讲师。2017－2018年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一项，湖南省教育厅一般项目一项。在《Inverse Problems in Science and Engineering》、《Applicable Analysis》、《Computers and Mathematics with applications》、《SIAM Journal on Imaging Sciences》、《SIAM Journal on Mathematical Analysis》发表论文六篇。