报告题目：Inverse Random Potential Scattering for Biharmonic Waves

报告时间：2022年11月15日（周二）上午9:00-10:00

腾讯会议：918-256-592

报告摘要：The scattering problems for the biharmonic wave equation have significant applications in thin plate elasticity. In this talk, we consider the inverse scattering problem for the biharmonic wave equation with a random potential, which is assumed to be a microlocally isotropic Gaussian rough field. Based on a new unique continuation principle, the well-posedness of the direct scattering problem is established in the distribution sense. For the inverse problem, the correlation strength of the random potential is shown to be uniquely determined by the high frequency limit of the second moment of the scattered field averaged over the frequency band. Moreover, we demonstrate that the expectation in the data can be removed and the data of a single realization is sufficient for the uniqueness of the inverse problem with probability one when the medium is lossless.

报告人简介：李培军，美国普渡大学数学系教授，2005年于美国密西根州立大学获得博士学位。其研究方向为科学计算、数值和数学分析、及偏微分方程的应用。具体领域包括偏微分方程反问题理论及计算，声波、弹性波及电磁波在复杂和随机介质中的散射和反散射问题。先后承担和主持了包括美国国家自然科学基金项目在内的共7项科研项目, 在SIAM J. Appl. Math.、SIAM J. Numer. Anal.、Inverse Problems等杂志发表论文百余篇。曾获美国国家自然科学基金杰出奖（NSF Career Award)及2015年度Calderon Prize，担任反问题领域有影响力期刊Inverse Problems and Imaging等多个国际期刊的编委。