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：董晓婧 博士（北京师范大学）
题 目：Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations
时 间：2021.11.20（星期六） 14:00-14:45
地 点：腾讯会议 628 746 726
摘 要：In this paper, we study the non relativistic limit and some properties of solutions for the following nonlinear Dirac equation. We show that solutions of nonlinear Dirac equation converge to the corresponding solutions of a coupled system of nonlinear Schrödinger equations as the speed of light tends to infinity for electrons with small mass. Moreover, we also prove the uniform boundedness and the exponential decay properties of the solutions for the nonlinear Dirac equation with respect to the speed of light c.
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报告人： 郭琪 博士（中国人民大学）
题 目: About Infinite-dimensional Hamiltonian Systems
时 间：2021.11.20（星期六） 14:50-15:35
地 点：腾讯会议 628 746 726
摘 要：In this paper, we will discuss some global properties of infinite-dimensional Hamiltonian systems. First, we will go over the general definition of infinite-dimensional Hamiltonian systems on Hilbert manifolds. Then we will give several examples from QFT, FM, etc. At last, we will explain how to study the existence and multiplicity of ground states for some variational problems from the view of infinite-dimensional Hamiltonian systems.
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报告人：余渊洋 博士（清华大学）
题 目：The concentration behavior of ground state solutions for nonlinear Dirac equation
时 间 ：2021.11.20（星期六） 15:40-16:25
地 点 ：腾讯会议 628 746 726
摘 要：In this talk, we consider the following nonlinear Dirac equation
where ε>0 is a small parameter, a>0 is a constant, α_1,α_2,α_3 and βare 4×4 Pauli-Dirac matrices, V ,Kand fare continuous but are not necessarily of class 
. We prove the existence of ground state solution by using variational methods, and we determine a concrete set related to the potentials V and K as the concentration position of these ground state solutions as ε→0. Moreover, we consider some properties of these ground state solutions, such as convergence and exponential decay estimate.
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