报告题目：Recent stability results for inverse potential problems

报 告 人：徐翔研究员（浙江大学）

报告时间：2025年5月10日  16:00-17:00

报告地点：格物楼528

报告摘要：

In this talk, we discuss some recent results for inverse potential problems. Considering an inverse elastic potential problem, we aims to reconstruct the potential utilizing the DtN map. For isotropic potential, we have derived a result of increasing stability, which consists of two parts:  a Holder type, and a logarithmic part that vanishes as the frequency increases. For anisotropic potential, by constructing different pairs of real and complex exponential solutions, we have derived a similar increase in stability for the linearized inverse problem. Moreover, based on the linearized problem, we proposed a reconstruction algorithm to recover the Fourier coefficients of the potential function’s elements and verified the effectiveness of the proposed algorithm by numerical examples. Furthermore, we consider a biharmonic Schrodinger operator, aiming to reconstruct the first-order perturbation term from the far-field data. A stability estimate for determining the divergence-free  of the first-order perturbation A through far-field data at multiple wavenumbers. Moreover, a similar algorithm is proposed to compute the Fourier coefficients. Numerical examples are conducted to verify the effectiveness of the algorithm.

报告人简介：

徐翔，浙江大学数学科学学院研究员。主要研究偏微分方程反问题的理论、算法及应用，曾在“第十一届应用反问题会议”(AIP2023)做大会报告。在SIAM J. Numer. Anal., SIAM J. Math. Anal., SIAM J. Appl. Math., Inverse Problems等国际知名期刊上发表论文40余篇，其中部分论文被列为ESI高引论文和Inverse Problems亮点收录。主持国家自然科学基金面上项目、作为子课题负责人参与国家重点研发计划、国家自然科学基金委创新群体研究项目、重大研究计划集成项目、国际(地区)合作项目等多项项目。2013年获得曙光青年学术奖，2014年入选“海外高层次人才计划青年项目”、浙江省特聘专家，2016年入选浙江省151人才工程。现任中国工业与应用数学学会反问题与成像专委会秘书长、浙江省数学会秘书长、《计算数学》编委等。