Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations
报告题目(Title)：Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations
报告人(Speaker)： 耿建生 教授 （南京大学）
地点(Place)：腾讯会议 会议 ID：794 196 226
时间(Time)：2021.7.2(周五下午)3:00-4:00
邀请人(Inviter)：黎雄
报告摘要
We prove an abstract infinite dimensional KAM theorem, which could be applied to prove the existence and linear stability of small-amplitude quasi-periodic solutions for one dimensional forced Kirchhoff equations with Dirichlet boundary conditions \[ u_{tt}-(1+\int_{0}^{\pi} |u_x|^2 dx)u_{xx}+M_\xi u+\epsilon g(\bar{\omega}t,x) =0,\quad u(t,0)=u(t,\pi)=0,\] where $M_\xi$ is a real Fourier multiplier, $g(\bar{\omega}t,x)$ is real analytic and odd in $x$ with forced Diophantine frequencies $\bar\omega\in \R^{\nu}$, $\epsilon$ is a small parameter.
The proof is based on an improved Kuksin lemma and the off-diagonal decay property of the forcing term. This is a joint work with Y. Chen.
主讲人简介
耿建生，南京大学数学系教授，博士生导师，曾获教育部新世纪优秀人才，教育部自然科学奖一等奖（排名第二）。主要研究哈密顿偏微分方程的拟周期解等；其研究成果发表在GAFA、Adv.Math、Comm.Math.Phys等国际著名杂志；曾受邀去意大利、加拿大、普林斯顿高等研究所工作访问。
