讲座题目：Linearized inverse Schrödinger potential problem with a large wave number 主讲人：陆帅 教授 主持人：朱升峰 副教授 开始时间🏇🏻：2020-10-28 14:30:00 结束时间🔎：2020-10-28 15:30:00 讲座地址：腾讯会议 ID🖕🏼🦹🏼：225 847 143 主办单位🕺：数学科学学院
报告人简介🏊🏿♀️： 陆帅👩🏼🎨🙇🏽♂️，复旦大学数学科学学院教授，主要从事数学物理反问题计算方法与数学理论的研究🧎，特别是反问题正则化方法收敛性分析及偏微分方程反问题稳定性理论等。至今在Inverse Problems、SIAM系列、Numer. Math.✍️、Math. Comp.等权威期刊共发表学术论文五十余篇⛪️，合作出版英文学术专著一本。2019年获得国家杰出青年科学基金资助🪁，现任《Inverse Problems》的编委💇♂️。
报告内容： We investigate recovery of the (Schrödinger) potential function from many boundary measurements at a large wave number. By considering such a linearized form, we obtain a Hölder type stability which is a big improvement over a logarithmic stability in low wave numbers. Furthermore, we extend the discussion to the linearized inverse Schrödinger potential problem with attenuation, where an exponential dependence of the attenuation constant is traced in the stability estimate. Based on the linearized problem, a reconstruction algorithm is proposed aiming at the recovery of the Fourier modes of the potential function. By choosing the large wave number appropriately, we verify the efficiency of the proposed algorithm by several numerical examples. It is a joint work with Victor Isakov (Wichita) and Boxi Xu (SUFE). |
