江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：New revival phenomena for the bidirectional dispersive evolution equations
报告人：康静，西北大学教授、博士生导师
报告时间：2023年4月21日19:00-20:00
腾讯会议：387-266-3917
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报告摘要： In this talk, the dispersive revival and fractalisation phenomena for the bidirectional dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles are investigated. Firstly, we study the periodic initial-boundary problem of the linear beam equation with step function initial data, and analyze the manifestation of the revival phenomenon for the corresponding solutions at rational times. Next, we extend the investigation to the periodic initial-boundary problems of the general bidirectional dispersive evolution equations. We prove that, if the initial functions are of bounded variation, the dynamical evolution of such periodic initial-boundary problem depend dramatically upon the associated dispersive relations. Integral polynomial or asymptotically integral polynomial dispersive relations produce dispersive revival/fractalization rational/irrational dichotomy effect. While, those with non-polynomial growth results in fractal profile all the time. Finally, numerical experiments are used to manifest how such effects persist into the nonlinear regime, in the concrete case of the nonlinear beam equation.
专家简介：康静，西北大学数学学院教授、博导。主要研究方向为数学物理和非线性可积系统。具体的研究课题包括：对称和李群在微分方程中的应用、非线性可积系统可积性及孤立波解、Liouville相关性理论及其应用。主持多项国家自然科学基金，一项陕西省自然科学基金杰出青年项目，入选“2017年度陕西省高校青年杰出人才支持计划”。