应兰州大学数学与统计学院魏婷教授、张正强副教授、张远祥副教授的邀请，南京航空航天大学龚荣芳教授将于2025年3月7-8日访问兰州大学，期间举办专题学术报告，欢迎全校师生参加。

报告题目:A study ofCauchy problem of the Helmholtz equation based on a relaxation model: regularization and analysis

时 间：2025年3月8日（星期六）8：30.

地 点：理工楼631

报告摘要：In this talk, we consider a Cauchy problem of the Helmholtz equation of recovering both missing voltage and current on inaccessible boundary from Cauchy data measured on the remaining accessible boundary. With an introduction of a relaxation parameter, the Dirichlet boundary conditions are approximated by two Robin ones. Associated with two mixed boundary value problems, a regularized Kohn-Vogelius formulation is proposed. Compared to the existing work, weaker regularity is required on the Dirichlet data and no Dirichlet BVPs needs to be solved. This makes the proposed model simpler and more efficient in computation. The well-posedness analysis about the relaxation model and error estimates of the corresponding inverse problem are obtained. A series of theoretical results are established for the new reconstruction model. Several numerical examples are provided to show feasibility and effectiveness of the proposed method.

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报告人简介

龚荣芳，南京航空航天大学数学学院，教授、博士生导师，江苏省计算数学分会常务理事。研究方向为医学成像、参数反演等数学物理反问题的正则化理论与数值方法。先后主持完成国家自然科学基金青年和面上项目、江苏省自然科学基金青年项目、科技部高端外国专家项目等，在Numerische Mathematik、Inverse Problems、Inverse Problems and Imaging、Communications in Computational Physics等期刊上发表SCI论文近40篇。

数学与统计学院

甘肃应用数学中心

萃英学院

2025年3月5日