佐治亚理工学院林治武教授学术报告 8月4日上午
发布时间: 2017-08-02 访问次数: 15

题目:Nonlinear Modulational Instability of Dispersive PDE Models

时间:2017849:00 - 11:00

地点:旗山校区理工北楼601报告厅

主讲:佐治亚理工学院林治武教授

主办:数学与计算机科学学院、福建省分析数学及应用重点实验室、数学研究中心

参加对象:感兴趣的教师和数学方向的研究生

专家简介:林治武,男,美国佐治亚理工学院教授、博士生导师,从事非线性分析及其应用领域的研究工作,在非线性波动方程解的稳定性、解的长时间行为方面作出一系列开创性的工作,研究成果发表在《CPAM》、 《CMP》、《ARMA》等学术期刊。

报告摘要:Joint with Jiayin Jin and Shasha Liao, we prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. Whitham equation, generalized KDV equation, Benjamin-Ono), nonlinear Schrödinger equation and BBM equation. First, the semigroup estimates required for the nonlinear proof are obtained by using the Hamiltonian structures of the linearized PDEs; Second, for KDV type equations the loss of derivative in the nonlinear term is overcome in two complementary cases. For smooth nonlinear term and general dispersive operators, we construct higher order approximation solutions and then use energy estimates to close it. For nonlinear terms of low regularity and with some additional assumption on the dispersive operators, we use a bootstrap argument to overcome the loss of derivative.