报告题目：Stochastic inverse problems for the biharmonic wave equation

报 告 人：李培军研究员（中国科学院数学与系统科学研究院）

报告时间：2024年3月16日  16:00-17:00

报告地点：格物楼528

报告摘要：

Stochastic inverse problems refer to inverse problems that involve uncertainties. Compared to deterministic counterparts, stochastic inverse problems are substantially more challenging due to the additional difficulties of randomness and uncertainties. In this talk, our recent progress will be discussed on some stochastic inverse problems for the biharmonic wave equation, which plays an important role in thin plate elasticity. I will present new models for the inverse random source and potential problems. Given the random source or potential, the direct problem is to determine the weve field; the inverse problem is to recover the unknown source or potential that generates the prescribed wave field. The well-posedness and regularity of the solutions will be addressed for the direct preblems. For the inverse problems, I will show that the microcorrelation strength of the random source or potential can be uniquely determined by the high frequency limit of the wave field at a single realization. I will also highlight ongoing projects on some direct and inverse scattering problems for biharmonic vaves.

报告人简介：

李培军，中国科学院数学与系统科学研究院研究员。2005年博士毕业干密歇根州立大学，2005年至2008年在密歇根大学从事博士后研究，2008年至2024年任职于普渡大学，2024年1月加入中国科学院数学与系统科学研究院。主要从事偏微分方程反问题、波动方程散射和反散射问题的理论、算法与应用研究。