题目：On generalized Holmgren’s principle to the Lamé operator with applications to inverse elastic problems

报告人：刁怀安 教授   吉林大学

摘要：This talk is concerned with the geometric properties of the (generalized) Lamé eigenfunction, where the Lamé operator arises in the theory of linear elasticity. We introduce the so-called homogeneous line segments of the Lamé eigenfunction in the underlying domain, on which the Lamé eigenfunction, its traction or their combination via an impedance parameter is vanishing. We give a comprehensive study on characterizing the presence of one or two such line segments and its implication to the uniqueness of the Lamé eigenfunction. The results can be regarded as generalizing the classical Holmgren’s uniqueness principle for the Lamé operator in two aspects. We establish the results by analyzing the development of analytic microlocal singularities of the Lamé eigenfunction with the presence of the aforesaid line segments. Finally, we apply the results to the inverse elastic problems in establishing two novel unique identifiability results. It is shown that a generalized impedance obstacle as well as its boundary impedance can be determined by using at most four far-field patterns. Unique determination by a minimal number of far-field patterns is a longstanding problem in inverse elastic scattering theory.

时间：2021.11.20，15:00-16:00

地点： 腾讯会议 会议ID：359357486

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刁怀安教授简介： 刁怀安，吉林大学威廉希尔中文网站教授，博士毕业于香港城市大学，研究兴趣为数值代数、随机化算法、偏微分算子谱理论、波散射问题，在Journal de Mathématiques Pures et Appliquées（JMPA）、Calculus of Variations and Partial Differential Equations（CVPDE）、Communications in Partial Differential Equations（CPDE）、Mathematics of Computation、SIAM Journal on Mathematics Analysis、Inverse Problems、Inverse problems and imaging、Numer. Linear Algebra Appl. 、BIT、Linear Algebra and its Applications以及机器学习领域顶级会议NeurIPS 2019等国际主流期刊发表科研论文50余篇，主持并完成国家自然科学基金委青年基金、数学天元基金以及教育部博士点新教师基金各一项，目前担任美国数学会评论员、中国仿真学会不确定系统分析与仿真专业委员会委员、 吉林省工业与应用数学学会第四届理事会理事。出版学术专著一本。曾多次受邀访问国内外高校进行合作研究与学术交流。