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：陈 昱 博士（北京师范大学）
题 目：Gradient estimates for Perfect conductivity problem and Lame system of linear elasticity
时 间：2020.10.17（星期六），09:30-10:30
地 点：腾讯会议 549 916 089
摘 要：In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the distance between two adjacent inclusions. This talk is concerned with gradient blow-up estimates for the perfect conductivity problem and the Lam\'{e} system of linear elasticity. we weaken the smoothness of the inclusions from to . In order to overcome this new difficulty, we take advantage of De Giorgi-Nash estimates, estimates and Campanato's approach to apply an adapted version of the iteration technique with respect to the energy. We establish the optimal gradient estimates, including upper and lower bounds, as well as an asymptotic formula of the gradient near the blow-up point.
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报告人： 李冏玥 博士（中山大学）
题 目：Asymptotic properties of the spinor field and the application to nonlinear Dirac models
时 间：2020.10.17（星期六），10:40-11:40
地 点：腾讯会议 549 916 089
摘 要：The Dirac equation is one of the basic equations in quantum mechanics. In this talk, we first discuss the asymptotic behavior of the solution to the Dirac equation in Minkowski space-time via a vector-field method. Based on the decay mechanism of the solution, we give a new insight to investigate the spinor null structure. Then a small-data-global-existence result of the nonlinear Dirac model follows.
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