暗网禁区 学术报告[2026] 009号

（高水平大学建设系列报告1268号）

报告题目：Babu\v{s}ka Problem in Composite Material and its Applications

报告人：李海刚 教授（北京师范大学）

报告时间：2026年1月19日 14:00-15:00

报告地点：汇文楼1420

报告内容：In this talk we study the interaction between two closely spaced rigid inclusions embedded in an elastic material or suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between them approaches zero. To effectively analyze the singular behavior of solutions, as well as to develop accurate numerical schemes, it is crucial to obtain higher-order derivative estimates --- both from an engineering perspective and for the requirements of numerical experiments. We derive optimal high-order derivative estimates for the Lam\’{e} system and Stokes equations in the presence of two rigid inclusions. For the Stokes equations, our approach resonates with the method used to handle the incompressibility constraint in the standard convex integration scheme.

报告人简介：李海刚，北京师范大学教授，博士生导师。主要从事材料科学中偏微分方程的理论研究，在复合材料中的Babuska问题、亚波长共振、流-固悬浮问题等方面取得系列进展，已在《Math. Ann.》《Adv. Math.》、《Arch. Ration. Mech. Anal.》、《J. Math. Pures Appl.》、 《Trans. AMS》等国际数学刊物发表论文50余篇。荣获教育部霍英东基金，教育部自然科学二等奖，北京市自然科学二等奖等奖励。

欢迎师生参加！

邀请人：龚华均

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