报告人:曾崇纯 教授（佐治亚理工大学）

报告题目：Instability, index theorems, and exponential dichotomy of Hamiltonian PDEs

报告摘要： Motivated by the stability/instability analysis of coherent states (standing waves, traveling waves, etc.) in nonlinear Hamiltonian PDEs such as BBM,GP, and 2-D Euler equations, we consider a general linear Hamiltonian system ut = JLu in a real Hilbert space X --the energy space. We obtain an index theorem which relates n¡(L) and the dimensions of subspaces of generalized

eigenvectors of some eigenvalues of JL, along with some information on such subspaces. Our third result is the linear exponential trichotomy of the group etJL.This includes the nonexistence of exponential growth in the finite co-dimensional invariant center subspace and the optimal bounds on the algebraic growth rate there. Next we consider the robustness of the stability/instability under small Hamiltonian perturbations. In particular, we give a necessary and sufficient condition on whether a purely imaginary eigenvalues may become hyperbolic under small perturbations. Finally we revisit some nonlinear Hamiltonian PDEs. This is a joint work with Zhiwu Lin.

报告人简介：佐治亚理工大学数学系教授。

报告时间: 2017年7月3日上午11:00-12:00

报告地点: 科技楼南楼702室