报告题目：Linearized Inverse Potential Problems at a High Frequency

报 告 人：许伯熹副教授（上海财经大学）

报告时间：2024年4月12日  11:00-11:40

报告地点：格物楼数学研究中心528报告厅

报告摘要：

We investigate the recovery of the potential function from many boundarymeasurements at a high frequency for linear or nonlinear equations. By consideringsuch a linearized form, we obtain Hölder type stability which is a big improvementover logarithmic stability in low frequencies. Increasing stability bounds for thesecoefficients contain a Lipschitz term with a factor growing polynomially in terms of the frequency, a Hölder term, and a logarithmic term that decays with respect to the frequency as a power. Based on the linearized problem, a reconstruction algorithm is proposed aiming at the recovery of sufficiently many Fourier modes of the potential function. By choosing the high frequency appropriately, the numerical evidence sheds light on the influence of the growing frequency and confirms the improved resolution.This is the joint work with Prof. Victor Isakov, Prof. Shuai Lu, Prof. Mikko Salo,and Mr. Sen Zou.

报告人简介：

许伯熹，理学博士，主要研究方向为数学物理反问题的理论与算法。2017年至今任上海财经大学数学学院副教授。在中国科学-数学、SISC、SIAP、SINUM、JCP、IP、IPI等国内外学术期刊发表论文十余篇。先后主持了国家自然科学基金面上项目与青年项目各1项，上海市科委科技人才计划1项。获第五届上海高校青年教师教学竞赛优秀奖。