理学院学术报告20201020
发布人:何杰  发布时间:2020-10-19   浏览次数:10

报告题目:Babuska Problem in Composite Materials and its Applications

报告人:李海刚 教授

 北京师范大学

报告时间:20201020日下午1330

报告地点:腾讯会议室960 832 620

报告摘要: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 Holder 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 willshow 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. Moreover, as a byproduct, we establish 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” in the shape optimizition of fibers.

 

报告人简介:李海刚,北京师范大学教授、博士生导师。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。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、流体-固体的悬浮问题等方面取得一系列进展:建立了高对比度复合材料应力集中的最佳爆破估计;揭示了内含物凸性在应力集中现象中的重要性,并得到应力的渐近展式;改进了经典的De Giorgi-Nash-Morser理论在分片常系数椭圆方程情形的正则性结果。已在《Adv. Math.》、《Arch. Ration. Mech. Anal.》、《J. Math. Pures Appl. 》、《Ann. Inst. H. Poincaré Anal. Non Linéaire》、《Calc. Var. & PDEs》、《Trans. AMS》、《SIAM J. Math. Anal.》等著名数学刊物发表论文30余篇。