报告题目：On the geometric structures of conductive transmission eigenfunctions and its application

报告人：刁怀安教授  东北师范大学

摘要：This talk is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were firstly studied in [1, Blåsten & Liu, JFA, 2017]. It is shown in two scenarios that the interior transmission eigenfunction must be locally vanishing near a corner of the domain with an interior angle less than $\pi$. We significantly extend and generalize those results in several aspects. First, we consider the conductive transmission eigenfunctions which include the interior transmission eigenfunctions as a special case. The geometric structures established for the conductive transmission eigenfunctions in this paper include the results in [1] as a special case. Second, the vanishing property of the conductive transmission eigenfunctions is established for any corner as long as its interior angle is not $\pi$. That means, as long as the corner singularity is not degenerate, the vanishing property holds. Third, the regularity requirements on the interior transmission eigenfunctions in [1] are significantly relaxed in the present study for the conductive transmission eigenfunctions. In order to establish the geometric properties for the conductive transmission eigenfunctions, we develop technically new methods and the corresponding analysis is much more complicated than that in [1]. Finally, as interesting and practical applications of the obtained geometric results, we establish a unique recovery result for the inverse scattering problem by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductivity.

报告时间：2019年6月14日(周五)上午10:30-11:30

报告地点：数学科学学院三楼报告厅

报告人简介：刁怀安，博士毕业于香港城市大学，东北师范大学数学与统计学院副教授，研究方向数值代数与反散射问题，在Mathematics of Computation, BIT, Numerical Linear Algebra with Applications, Linear Algebra and its Applications等国际知名期刊发表科研论文三十余篇；出版学术专著一本；曾主持国家自然科学基金青年基金项目1项，数学天元基金1项，教育部博士点新教师基金1项；现为吉林省工业与应用数学学会第四届理事会理事,国际线性代数系会会员；曾多次赴普渡大学、麦克马斯特大学、汉堡工业大学、日本国立信息研究所、香港科技大学、香港浸会大学等高校进行合作研究与学术访问。据Web of Science显示他的单篇论文最高被引用51次。