报告题目：Babuska Problem in Composite Materials and Suspension Problem in Stokes Flow
时 间：2022年4月6日（星期三）上】下午3：30
地 点：腾讯ID: 706346906
主 办：数学与统计学院、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、 福建师范大学数学研究中心
参加对象：感兴趣的老师和学生
报告摘要：In a two-phase composite, the study of its effective property is a central topic in material sciences. Especially, in a high-contrast elastic composite media, when inclusions are spaced closely, the stress always concentrates in between inclusions and causes damage initiation. This local concentration phenomenon essentially affects the global properties of the composite. For Babuska problem in linear elasticity, we obtain the blow-up asymptotic expressions of the gradients of solutions to the Lame system with partially infinite coefficients in the narrow region when the distance between inclusions tends to zero. We then apply it to prove an extended Flaherty-Keller formula on the effective elastic property of a periodic composite with densely packed fibers, which is related to the “Vigdergauz microstructure”, possessing optimality properties in the context of Hashin-Shtrickmann bounds in structural optimization problems. Recently, we completely solve the stress concentration problem between two adjacent rigid inclusions suspending in the Stokes flow.
报告人简介：李海刚，北京师范大学数学科学学院教授、博士生导师，教育部青年长江学者。主要从事材料科学中的偏微分方程理论研究，在复合材料中的Babuska问题、流-固模型的悬浮问题等方面取得一系列进展，已在Adv Math、ARMA、JMPA、JFA、AIHP-NL、SIMA、TAMS、CV&PDEs等国际权威数学杂志发表论文30余篇。2016年获得霍英东青年教师基金，2018年获得教育部自然科学二等奖。2020年入选教育部长江学者奖励计划青年学者。