学术报告
报告题目： Higher-dimensional Dispersive Quantization
报告人：康静，西北大学教授、博士生导师、陕西省杰青
报告时间：2021年11月4日18:00-18:30
腾讯会议 ID： 881 204 471
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报告摘要：In this talk, we investigate the dispersive quantization of the two-dimensional linear dispersive equations subject to the periodic initial-boundary value problem over a bounded domain on the plane. We first study the periodic initial-boundary value problem for the two-dimensional linear KdV equation on a rectangle domain. We show that the piecewise constant initial data leads to quantized structures at rational times, meaning that the solution is piecewise constant on rational sub-rectangle. Furthermore, we verify these results extend to general two-dimensional linear dispersive equations with “integral polynomial” dispersion relations, subject to a more general piecewise smooth initial condition. The solution is a linear combination of finitely many translates of the initial data. Finally, we study the fractal structure of the solutions at irrational times.
专家简介： 康静，西北大学마카오 슬롯 머신 잭팟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”。