中科院数学与系统科学研究院

数学研究所

 

非线性分析研讨班

 

报告人Prof. Haigang LiBeijing Normal University

 Babuska Problem in Composite Materials and its Applications

  2019.10.17(星期四),11 :15-12 :15

  点:数学院南楼N224

  要:In high-contrast composite materials, the stress concentration is a common phenomenon when inclusions are densely distributed and may possibly touch. It always causes damage initiation and even ultimate failure. This problem was proposed mathematically by Ivo Babuska, concerning the system of linear elasticity, modeled by a class of second order elliptic systems of divergence form with discontinuous coefficients. I will first review some of our results on upper and lower bounds of the grdients by developing an iteration technique with respect to the energy integral to overcome the essential difficulty from the lack of maximal principle for elliptic systems, then present our very recent results on asymptotics of the gradients in dimensions two and three to show the key role of the geometry of the inclusions played in such blow-up analysis.

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