报告题目：Inverse elastic scattering for a random potential

报告人：王旭 副研究员 中国科学院数学与系统科学研究院

照片：

邀请人：冯晓莉 副教授

报告时间：2022年5月23日上午9：30

腾讯会议ID：945-913-149

报告人简介：王旭，中科院科学院数学与系统科学研究院优秀青年副研究员，2018年博士毕业于中科院数学与系统科学研究院，2018-2021在美国普渡大学做博士后。主要从事随机偏微分方程反问题、随机偏微分方程数值方法研究。在SIAM J. Numer. Anal.，SIAMJ. Sci. Comput.，SIAM J. Appl. Math.，Inverse Problems等重要期刊发表论文十余篇，合著有一本学术专著《Lecture Notes in Mathematics 2251》，并于Springer出版社出版。

报告摘要：This talk is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a rough potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian random field with the covariance operator being described by a classical pseudo-differential operator. The goal is to determine the principal symbol of the covariance operator from the scattered wave measured in a bounded domain which has a positive distance from the domain of the potential. For such a rough potential, the well-posedness of the direct scattering problem in the distribution sense is established by studying an equivalent Lippmann– Schwinger integral equation. For the inverse scattering problem, it is shown with probability one that the principal symbol of the covariance operator can be uniquely determined by the amplitude of the scattered waves averaged over the frequency band from a single realization of the random potential. The analysis employs the Born approximation in high frequency, asymptotics of the Green tensor for the elastic wave equation, and microlocal analysis for the Fourier integral operators.

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