Computational & Applied Math Seminar

Inverse Random Source Problems for Wave Equations

  • 演讲者:Peijun Li(普渡大学)

  • 时间:2021-12-08 14:00-15:00

  • 地点:慧园3栋 415报告厅

Abstract 
Motivated by significant applications, the inverse source problem remains an important and active research subject in inverse scattering theory. The inverse random source problem refers to the inverse source problem that involves uncertainties, and is substantially more challenging than its deterministic counterpart.  

In this talk, our recent progress will be discussed on inverse source problems for the stochastic wave equations. I will present a new model for the random source, which is assumed to be a microlocally isotropic Gaussian random field such that its covariance operator is a classical pseudo-differential operator. The well-posedness and regularity of the solution will be addressed for the direct problem. For the inverse problem, it is shown that the principal symbol of the covariance operator can be uniquely determined by the high frequency limit of the wave field at a single realization. I will also highlight some ongoing and future projects in the inverse random potential and medium problems. 


Short bio 
 李培军, 2005 年毕业于美国密西根州立大学获博士学位,现任普渡大学数学系教授。 主要从事科学计算、数值分析和偏微分方程反问题等方面的工作, 特别是光学、电磁学和波动方程中正反散射问题的研究。先后承担和主持了 5 项美国国家自然科学基金项目,在包括 Inverse Problems,SIAM J. Numer. Anal. 等在内的国际期刊上发表论文 80 余篇。曾获美国国家自然科学基金杰出奖项(NSF Career Award)及 2015 年度 Calderon Prize.