講座主題：Inverse random source problems for time-harmonic acoustic and elastic waves
主講人：李建樑
工作單位：長沙理工大學
講座時間：2019年12月26日（周四）下午4:30--5:30
講座地點：數學院大會議室341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
李建樑，中國科學院大學理學博士。2014年7月起任長沙理工大學數學與統(tǒng)計學院講師。2017－2018年受國家留學基金委資助赴美國普渡大學數學系訪問一年。主要研究領域為反散射問題的理論與數值方法、隨機反散射問題的理論研究。主持國家自然科學基金青年項目一項，湖南省教育廳一般項目一項。在《Inverse Problems in Science and Engineering》、《Applicable Analysis》、《Computers and Mathematics with applications》、《SIAM Journal on Imaging Sciences》、《SIAM Journal on Mathematical Analysis》發(fā)表論文六篇。
