江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：New revival phenomena for the bidirectional dispersive evolution equations
報告人：康靜，西北大學教授、博士生導師
報告時間：2023年4月21日19:00-20:00
騰訊會議：387-266-3917
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報告摘要： 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.
專家簡介：康靜，西北大學伟德bv教授、博導。主要研究方向為數學物理和非線性可積系統。具體的研究課題包括：對稱和李群在微分方程中的應用、非線性可積系統可積性及孤立波解、Liouville相關性理論及其應用。主持多項國家自然科學基金，一項陝西省自然科學基金傑出青年項目，入選“2017年度陝西省高校青年傑出人才支持計劃”。