會(huì)議主題： 動(dòng)力系統(tǒng)與偏微分方程及其應(yīng)用
主 講 人： 儲(chǔ)繼峰、馮兆生、李萬同、宋永利、王智誠、張文萌
講座時(shí)間：2020年10月26日上午9:00-17:05
講座地點(diǎn)：X2511
講座題目：1、Rotational steady waves in two-layer flows
2、Wave Equation with van der Pol Boundary Condition
3、Spatial Propagation of Nonlocal Dispersal Equations
4、Spatiotemporal dynamics in the single population model with
memory-based diffusion and nonlocal effect
5、Time periodic traveling wave solutions for a Kermack-McKendrick
epidemic model with diffusion and seasonality
6、光滑線性化問題的最新進(jìn)展
講座內(nèi)容：
ROTATIONAL STEADY WAVES IN TWO-LAYER FLOWS
儲(chǔ)繼峰 教授 上海師范大學(xué)
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 (李萬同)
Lanzhou University （蘭州大學(xué)）
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
杭州師范大學(xué)
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
王智誠 教授
蘭州大學(xué)
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 $c^*$.
光滑線性化問題的最新進(jìn)展
張文萌 教授 重慶師范大學(xué)
摘 要：光滑線性化問題是動(dòng)力系統(tǒng)理論中的基本問題，在Poincare，Sternberg，Hartman—Grobman等著名數(shù)學(xué)家開創(chuàng)性研究的基礎(chǔ)之上，近年來人們針對(duì)線性化的光滑性和非共振條件取得了一系列重要結(jié)果。在這次報(bào)告中我們將介紹相關(guān)進(jìn)展。
主講人簡(jiǎn)介：
儲(chǔ)繼峰教授簡(jiǎn)介
儲(chǔ)繼峰，上海師范大學(xué)數(shù)學(xué)系教授，博士研究生導(dǎo)師。2008年7月獲清華大學(xué)理學(xué)博士學(xué)位，從事常微分方程和動(dòng)力系統(tǒng)及其應(yīng)用的研究工作，在“低自由度保守系統(tǒng)的運(yùn)動(dòng)穩(wěn)定性”、“線性系統(tǒng)基本動(dòng)力學(xué)量及其應(yīng)用”、“海洋流體動(dòng)力學(xué)”等三個(gè)方面都做了一些探索。先后入選教育部“新世紀(jì)優(yōu)秀人才支持計(jì)劃”、江蘇省第四期“333高層次人才培養(yǎng)工程”、“德國洪堡學(xué)者”，并榮獲教育部“霍英東高校青年教師獎(jiǎng)”、“山東省自然科學(xué)二等獎(jiǎng)”。先后主持國家自然科學(xué)基金青年項(xiàng)目1項(xiàng)、國家自然科學(xué)基金面上項(xiàng)目3項(xiàng)。
李萬同教授簡(jiǎn)介
李萬同，二級(jí)教授，博士，博士導(dǎo)師，蘭州大學(xué)“萃英學(xué)者”二級(jí)教授，蘭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院院長(zhǎng)、中國數(shù)學(xué)會(huì)副理事長(zhǎng)、甘肅省數(shù)學(xué)會(huì)理事長(zhǎng)，甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)重點(diǎn)實(shí)驗(yàn)室主任。主要從事偏微分方程與動(dòng)力系統(tǒng)領(lǐng)域的相關(guān)研究，合作在Marcel Dekker出版社《純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué)專著系列》出版專著1部，主持國家自然科學(xué)基金重點(diǎn)項(xiàng)目1項(xiàng)，面上及國際合作項(xiàng)目6項(xiàng)，參加重點(diǎn)項(xiàng)目1項(xiàng)。主持完成的項(xiàng)目獲甘肅省自然科學(xué)一等獎(jiǎng)和二等獎(jiǎng)各1次。2001年獲《教育部高等學(xué)校優(yōu)秀青年教師教學(xué)科研獎(jiǎng)勵(lì)計(jì)劃》既第二屆《教育部?jī)?yōu)秀青年教師獎(jiǎng)》，并獲《甘肅省優(yōu)秀專家》，2004年獲國務(wù)院頒發(fā)的政府特殊津貼并獲《寶鋼教育基金會(huì)優(yōu)秀教師獎(jiǎng)》、2009年入選甘肅省領(lǐng)軍人才第一層次。2013年應(yīng)邀在第六屆世界華人數(shù)學(xué)家大會(huì)做邀請(qǐng)報(bào)告。
馮兆生教授簡(jiǎn)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.
宋永利教授簡(jiǎn)介
宋永利教授，2005 年于上海交通大學(xué)獲博士學(xué)位，先后在同濟(jì)大學(xué)和杭州師范大學(xué)工作。2011 年起任同濟(jì)大學(xué)博士生指導(dǎo)教師。曾出訪西班牙、澳大利亞、加拿大、美國做博士后或合作研究。現(xiàn)為兩個(gè)國際學(xué)術(shù)期刊編委。已在國際學(xué)術(shù)期刊上發(fā)表學(xué)術(shù)論文70余篇。連續(xù)多年入選中國高被引學(xué)者榜單(數(shù)學(xué)類)。曾主持、或作為項(xiàng)目組主要成員參與完成國家自然科學(xué)基金重點(diǎn)項(xiàng)目、面上項(xiàng)目、上海市自然科學(xué)項(xiàng)目等十余項(xiàng)。目前正在主持一項(xiàng)國家自然科學(xué)基金面上項(xiàng)目的研究工作。2011年入選教育部新世紀(jì)優(yōu)秀人才計(jì)劃。2017年獲威海市科學(xué)技術(shù)一等獎(jiǎng)，2018年入選浙江省“錢江學(xué)者”特聘教授。2018年入選浙江省151人才工程第一層次培養(yǎng)人選、2020年獲杭州市優(yōu)秀教師稱號(hào)。
王智誠教授簡(jiǎn)介
王智誠，男，甘肅莊浪人，蘭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，甘肅省飛天學(xué)者特聘教授，博士生導(dǎo)師。1994年本科畢業(yè)于西北師范大學(xué)，2007年在蘭州大學(xué)獲理學(xué)博士學(xué)位，2008年3月至2009年3月在加拿大約克大學(xué)從事博士后工作一年，2014年到法國波爾多大學(xué)訪問。在Trans. AMS、SIAM J. Math. Anal.、SIAM J. Appl. Math.、JMPA、Calc. Var. PDE、JDE、JDDE、Nonlinearity、J. Math. Biol.、J. Nonlinear Sci、Proc. Royal. Soc. A等雜志發(fā)表SCI論文80多篇。2010年入選教育部新世紀(jì)優(yōu)秀人才支持計(jì)劃，2011和2019年分別獲得甘肅省自然科學(xué)二等獎(jiǎng)，2016年入選甘肅省飛天學(xué)者特聘教授，主持完成兩項(xiàng)國家自然科學(xué)基金面上項(xiàng)目以及教育部博士點(diǎn)基金等多項(xiàng)省部級(jí)項(xiàng)目，正在參加一項(xiàng)國家自然科學(xué)基金重點(diǎn)項(xiàng)目。目前擔(dān)任兩個(gè)SCI雜志International J. Bifurc. Chaos 和Mathematical Biosciences and Engineering (MBE) 的編委（Associate editor）。
張文萌教授簡(jiǎn)介
張文萌，重慶師范大學(xué)教授，碩士生導(dǎo)師。分別于2011年和2012年在波蘭綠山大學(xué)和四川大學(xué)取得博士學(xué)位，從2012年開始在重慶師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院工作，主要從事的研究領(lǐng)域?yàn)槲⒎址匠膛c動(dòng)力系統(tǒng)，重點(diǎn)關(guān)注其中的線性化與不變流形等問題。近年來，在該研究領(lǐng)域取得一系列重要成果，在美國Trans. Amer. Math.、Soc.、Adv. Math.、Math. Ann.等期刊上發(fā)表論文17篇。先后主持國家自然科學(xué)基金面上項(xiàng)目和青年項(xiàng)目等省部級(jí)以上項(xiàng)目6項(xiàng)，參與國家自然科學(xué)基金重點(diǎn)項(xiàng)目1項(xiàng)，獲2019國家優(yōu)秀青年科學(xué)基金項(xiàng)目資助，部分成果獲2018年度教育部自然科學(xué)一等獎(jiǎng)（排名第2），并入選重慶市第四批高層次人才特殊支持計(jì)劃（科技創(chuàng)新領(lǐng)軍人才）。
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