Inverse random scattering problems for the fractional Helmholtz equation

报告题目: Inverse random scattering problems for the fractional Helmholtz equation

报告人：李镇乾 博士后 中国科学院数学与系统科学研究院

报告时间：2026年3月20日下午14:30-15:30

报告地点：红瓦楼726

报告内容简介：We study inverse random source and potential scattering problems for the fractional Helmholtz equation. The potential and source terms are modeled as centered microlocally isotropic generalized Gaussian fields, whose covariance and relation operators are classical pseudo-differential operators. For the direct scattering problem, we establish existence and uniqueness of distributional solutions for sufficiently large wavenumbers. We then prove uniqueness results for recovering the microlocal strengths of both operators from a single realization of scattering data. For the inverse potential problem, two measurement settings are considered: near-field data generated by a point source incidence and far-field patterns corresponding to plane wave illumination. The inverse source problem is recovered by far-field patterns. The analysis combines the Born approximation, microlocal arguments, asymptotics of the fractional Green's function, and Fourier analytic techniques.

报告人简介：李镇乾，2019年本科毕业于中国科学院大学，2024年博士毕业于中国科学院数学与系统科学研究院，现为中国科学院数学与系统科学研究院计算数学与科学工程计算研究所博士后。主要研究方向为随机波动方程反散射问题。

报告邀请人：赵娜