报告人：李海刚教授 北京师范大学太阳成集团tyc411

报告时间：2021/06/25 14:00-16:00

地点：腾讯会议

会议链接：https://meeting.tencent.com/s/0KNsIwrOer5X

会议 ID：408 379 459

摘要：A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composite with densely packed inclusions whose material properties differ from that of the background. For a general elliptic system, when the coefficients are piecewise H\”older continuous and uniformly bounded, an ε-independent bound of the gradient was obtained by Li and Nirenberg, where ε represents the distance between the interfacial surfaces. However, in high-contrast composites, when ε tends to zero, the stress always concentrates in the narrow regions. As a contrast to the uniform boundedness result of Li and Nirenberg, in order to investigate the role of ε played in such kind of concentration phenomenon, in this talk we will show the blow-up asymptotic expressions of the gradients of solutions to the Lame system with partially infinite coefficients in dimensions two and three. This completely solves the Babuska problem on blow-up analysis of stress concentration in high-contrast composite media. Recently, we extend our method to deal with the resonant behavior between two close-to-touching convex acoustic subwavelength resonators.

报告人简介：李海刚博士主要从事材料力学和几何学中偏微分方程理论研究。在复合材料中的Babuska问题、Monge-Ampere方程和Hessian方程外Dirichlet问题等方面做出一系列深刻的原创性成果，在《Adv.Math.》(2篇)、《Arch. Ration. Mech. Anal.》(2篇)、《J. Math. Pures Appl.》(独立)、《Trans. Amer. Math. Soc.》、《Calc. Var. Partial Differential Equations》(2篇)、《SIAM J.Math. Anal.》(3篇)、《J. Differential Equations》等SCI国际主流数学杂志上发表科研论文30余篇。2007年国家建设高水平大学首批公派研究生，北京师范大学与美国罗格斯（Rutgers）大学联合培养博士（导师：李岩岩教授、保继光教授），2009年博士毕业留校工作。国家自然基金面上项目主持人（2016-2019，2020-2023），国家自然基金重点项目主要成员（2017-2021）。2016年获得教育部霍英东青年教师基金。2018年获得教育部自然科学二等奖。

联系人：赖俊（laijun6@zju.edu.cn）

欢迎参加！