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。