中科院数学与系统科学研究院
数学研究所
学术报告
非线性分析研讨班
时 间：2022.09.02（星期五）
地 点：思源楼 S817
n 下午14:00-14:40
报告人：郭琪 博士（中国人民大学）
题 目：Some examples of Infinite-dimensional Hamiltonian Systems
摘 要：In this talk, we will explain what is an infinite-
dimensional Hamiltonian system and how to use variational methods to study the system. First, we go over the general definition of IDHS on linear spaces and infinite-dimensional manifolds. Then we will give several examples from QFT, FM, etc. At last, we will show some local properties of IHDS via variational methods.
n 下午14:40-15:20
报告人：董晓婧 博士（北京师范大学）
题 目：A new survey on nonlinear Dirac equations
摘 要：In this talk, we study stationary solutions for nonlinear Dirac systems from three aspects. First, we answer the question that what happens when two components of spinors equal zero. All the cases is considered and we find only two cases have nontrivial solutions and these solutions satisfy nonlinear Dirac equation with lower dimension. Then, we study the existence and nonexistence of solutions for the case that ωdoes not belong to (−mc^2, mc^2). At last, we give a general method to show the nonexistence of special solutions to the nonlinear Dirac systems. Here, nonexistence means no nontrivial solutions.
n 下午15:20-16:00
报告人：余渊洋 博士（清华大学）
题 目：Normalized solitary wave solutions of a nonlinear Dirac equation
摘 要：In this talk, we consider a class of nonlinear Dirac equation. We present a new approach which is based on the perturbation arguments and show the existence of L^2-normalized solitary wave solutions of a class of nonlinear Dirac equation by variational methods.
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