题    目：An inverse obstacle problem with a single pair of Cauchy data

主讲人：徐小绪 副教授

单    位：西安交通大学

时    间：2025年1月21日 10:00

腾讯ID：710-755-506

密    码：250121

摘    要：This talk is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy data. Uniqueness results are established under some a priori assumptions on the input boundary value data. A domain-defined sampling method, based on the factorization method originating from inverse acoustic scattering, has been proposed to recover both the constant conductivity coefficient and the polygonal obstacle. A hybrid strategy, which combines the sampling method and iterative scheme, is employed to reconstruct the location and shape of the obstacle. Numerical examples indicate that our method is efficient. This talk is based on a joint work with Guanghui Hu.

简    介：徐小绪，西安交通大学副教授，博士生导师，毕业于中国科学院数学与系统科学研究院，于2019年获博士学位，现就职于西安交通大学数学与统计学院，入选西安交通大学青年拔尖人才支持计划和思源学者挖潜支持计划以及陕西省科协青年人才托举计划，曾获得中国科学院院长特别奖、中国科学院优秀博士学位论文奖，研究兴趣包括波的传播与反演、反散射问题的理论与算法、偏微分方程反问题等。目前共承担包括国家自然科学基金在内的共6项科研项目，曾在SIAM J. Appl. Math.和SIAM J. Imaging Sci.等期刊发表数篇论文。