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国家自然科学基金申报系列讲座——动力系统与偏微分方程及其应用

来源:   作者:     日期:2020-10-25 10:22:35   点击数:  

会议主题: 动力系统与偏微分方程及其应用


人: 储继峰、冯兆生、李万同、宋永利、王智诚、张文萌


讲座时间:20201026日上午9:00-17:05


讲座地点:X2511


讲座题目:1Rotational steady waves in two-layer flows


2Wave Equation with van der Pol Boundary Condition


3Spatial Propagation of Nonlocal Dispersal Equations


4Spatiotemporal dynamics in the single population model with

memory-based diffusion and nonlocal effect


5Time periodic traveling wave solutions for a Kermack-McKendrick

epidemic model with diffusion and seasonality


6、光滑线性化问题的最新进展



讲座内容:

ROTATIONAL STEADY WAVES IN TWO-LAYER FLOWS
储继峰 教授 上海师范大学

Abstract

We will present two reformulations for steady periodic water waves in two-layer flows. Then we present a variational formulation by showing that critical points of a natural energy functional are solutions to the governing equations. Provided that there are no stagnation points in the flow, we show that each streamline, including the free surface and the interface, is a real analytic curve if the height function has suitable regularity.



Wave Equation with van der Pol Boundary Condition

Zhaosheng Feng


School of Mathematical and Statistical Sciences, University of Texas-RGV, Edinburg, Texas 78539, USA


Abstract

In this talk, we consider the one-, two- and three-dimensional wave equation on the unit interval [0, 1] with a van der Pol type condition. This nonlinear boundary condition behaves like a van der Pol oscillator, causing the total energy to rise and fall within certain bounds regularly or irregularly. We formulate the problem in terms of an equivalent first order hyperbolic system and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary conditions. Qualitative and numerical techniques are developed to tackle the cubic nonlinearities and the chaotic regime is determined. Numerical simulations and visualizations of chaotic vibrations are illustrated by computer graphics.


Spatial Propagation of Nonlocal Dispersal Equations

Wan-Tong Li (李万同)

Lanzhou University (兰州大学)

Abstract

In this talk, I will report the spatial propagation for nonlocal dispersal equations. It consists of five parts. I first will present some relations between local (random) and nonlocal dispersal problems and then I will report our recent results on the spatial propagation (traveling waves and entire solutions) of nonlocal dispersal equations. Part III is concerned with acceleration propagation for nonlocal dispersal systems. Part IV is concerned with free boundary problems on nonocal dispersal equations. In Part IV, I list some problems on nonlocal dispersal equations.


Spatiotemporal dynamics in the single population model with memory-based diffusion and nonlocal effect

宋永利 特聘教授

杭州师范大学

Abstract

To incorporate spatial memory and nonlocal effect of animal movements, we propose and investigate the spatiotemporal dynamics of the single population model with memory-based diffusion and nonlocal reaction. We first study the stability of a positive equilibrium and the steady state bifurcation induced by diffusion and nonlocality. We then investigate the impact of the averaged memory period on stability and bifurcation, and show that the combination of the averaged memory period and the diffusion can lead to the occurrence of Turing-Hopf and double Hopf bifurcations. The paper originally derives the normal form theory for Turing-Hopf bifurcation in the general reaction-diffusion equation with memory-based diffusion and nonlocal reaction. This novel algorithm can be widely used to classify the spatiotemporal dynamics near the Turing-Hopf bifurcation point. Finally, we apply the obtained results to a model proposed by Brit-ton and numerically illustrate the spatiotemporal patterns induced by Hopf, Turing-Hopf and double Hopf bifurcations. Stable spatially homogeneous/nonhomogeneous periodic solutions, homogeneous/nonhomo-geneous steady states and the transition from one of these solutions to another are provided in this paper. We additionally acquire the coexistence of two stable spatially nonhomogeneous steady states or two spatially nonhomogeneous periodic solutions near the Turing-Hopf bifurcation point.



Time periodic traveling wave solutions for a Kermack-McKendrick epidemic model with diffusion and seasonality

王智诚 教授

兰州大学

Abstract

This talk is concerned with time periodic traveling wave solutions for a Kermack-McKendrick SIR epidemic model with individuals diffusion and environment heterogeneity. In terms of the basic reproduction number $R_0$ of the corresponding periodic ordinary differential model and the minimal wave speed $c^*$, we establish the existence of periodic traveling wave solutions by the method of super- and sub-solutions, the fixed point theorem, as applied to a truncated problem on a large but finite interval, and the limiting arguments. We further obtain the non-existence of periodic traveling wave solutions for two cases involved with $R_0$ and $c^*$.

光滑线性化问题的最新进展
张文萌 教授 重庆师范大学


:光滑线性化问题是动力系统理论中的基本问题,在PoincareSternbergHartman—Grobman等著名数学家开创性研究的基础之上,近年来人们针对线性化的光滑性和非共振条件取得了一系列重要结果。在这次报告中我们将介绍相关进展。




主讲人简介:


储继峰教授简介

储继峰,上海师范大学数学系教授,博士研究生导师。20087月获清华大学理学博士学位,从事常微分方程和动力系统及其应用的研究工作,在低自由度保守系统的运动稳定性线性系统基本动力学量及其应用海洋流体动力学等三个方面都做了一些探索。先后入选教育部新世纪优秀人才支持计划、江苏省第四期“333高层次人才培养工程德国洪堡学者,并荣获教育部霍英东高校青年教师奖山东省自然科学二等奖。先后主持国家自然科学基金青年项目1项、国家自然科学基金面上项目3项。


李万同教授简介

李万同,二级教授,博士,博士导师,兰州大学萃英学者二级教授,兰州大学数学与统计学院院长、中国数学会副理事长、甘肃省数学会理事长,甘肃省高校应用数学与复杂系统重点实验室主任。主要从事偏微分方程与动力系统领域的相关研究,合作在Marcel Dekker出版社《纯粹数学与应用数学专著系列》出版专著1部,主持国家自然科学基金重点项目1项,面上及国际合作项目6项,参加重点项目1项。主持完成的项目获甘肃省自然科学一等奖和二等奖各1次。2001年获《教育部高等学校优秀青年教师教学科研奖励计划》既第二届《教育部优秀青年教师奖》,并获《甘肃省优秀专家》,2004年获国务院颁发的政府特殊津贴并获《宝钢教育基金会优秀教师奖》、2009年入选甘肃省领军人才第一层次。2013年应邀在第六届世界华人数学家大会做邀请报告。


冯兆生教授简介

Zhaosheng Feng is a full-professor at the School of Mathematical and Statistical Sciences of University of Texas-RGV, Edinburg, Texas 78539, USA. His research interests include nonlinear analysis, dynamical systems, computational methods, mathematical physics and mathematical biology etc.


宋永利教授简介

宋永利教授,2005 年于上海交通大学获博士学位,先后在同济大学和杭州师范大学工作。2011 年起任同济大学博士生指导教师。曾出访西班牙、澳大利亚、加拿大、美国做博士后或合作研究。现为两个国际学术期刊编委。已在国际学术期刊上发表学术论文70余篇。连续多年入选中国高被引学者榜单(数学类)。曾主持、或作为项目组主要成员参与完成国家自然科学基金重点项目、面上项目、上海市自然科学项目等十余项。目前正在主持一项国家自然科学基金面上项目的研究工作。2011年入选教育部新世纪优秀人才计划。2017年获威海市科学技术一等奖,2018年入选浙江省钱江学者特聘教授。2018年入选浙江省151人才工程第一层次培养人选、2020年获杭州市优秀教师称号。


王智诚教授简介

王智诚,男,甘肃庄浪人,兰州大学数学与统计学院教授,甘肃省飞天学者特聘教授,博士生导师。1994年本科毕业于西北师范大学,2007年在兰州大学获理学博士学位,20083月至20093月在加拿大约克大学从事博士后工作一年,2014年到法国波尔多大学访问。在Trans. AMSSIAM J. Math. Anal.SIAM J. Appl. Math.JMPACalc. Var. PDEJDEJDDENonlinearityJ. Math. Biol.J. Nonlinear SciProc. Royal. Soc. A等杂志发表SCI论文80多篇。2010年入选教育部新世纪优秀人才支持计划,20112019年分别获得甘肃省自然科学二等奖,2016年入选甘肃省飞天学者特聘教授,主持完成两项国家自然科学基金面上项目以及教育部博士点基金等多项省部级项目,正在参加一项国家自然科学基金重点项目。目前担任两个SCI杂志International J. Bifurc. Chaos Mathematical Biosciences and Engineering (MBE) 的编委(Associate editor)。


张文萌教授简介

张文萌,重庆师范大学教授,硕士生导师。分别于2011年和2012年在波兰绿山大学和四川大学取得博士学位,从2012年开始在重庆师范大学数学科学学院工作,主要从事的研究领域为微分方程与动力系统,重点关注其中的线性化与不变流形等问题。近年来,在该研究领域取得一系列重要成果,在美国Trans. Amer. Math.Soc.Adv. Math.Math. Ann.等期刊上发表论文17篇。先后主持国家自然科学基金面上项目和青年项目等省部级以上项目6项,参与国家自然科学基金重点项目1项,获2019国家优秀青年科学基金项目资助,部分成果获2018年度教育部自然科学一等奖(排名第2),并入选重庆市第四批高层次人才特殊支持计划(科技创新领军人才)。



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主办:西南交通大学数学学院数学系