Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations

报告主题：Linearly Stable KAM Tori for One Dimensional Forced Kirchhoff Equations

报告人：耿建生

报告时间：2020年9月25日 9:00-10:00

地点：腾讯会议 ID：712 478 783

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.

报告人简介：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。