题目一：Traveling Wave Solutions of Modified Nesterenko-Type Equation: Dynamical System Approach
内容简介：This overview paper reviews a dynamical systems approach to studying the singular nonlinear traveling wave equations. First, the notion of exact peakon, periodic peakon, pseudo-peakon, as well as compacton solutions for the generalized Camassa–Holm (CH) equation and the Degasperis–Procesi (DP) equation, is introduced. Based on the method of dynamical systems and the theory of singular traveling wave equations, the exact explicit parametric representations of the solutions of the above-mentioned equations are derived. These solutions show that peakon is a limit solution of a family of periodic peakons or a limit solution of a family of pseudo-peakons in different limit senses, whereas the pseudo-peakon and pseudo-periodic peakon families are smooth classical solutions in two different time scales. Second, nonlinear wave equation models are introduced to show that there exist various exact explicit peakon solutions, which are different from the peakon solution given by the generalized CH equation and the DP equation. Third, the so-called “peakon equations” discussed in some studies actually have no peakons. Corresponding to these “peakon equations”, their traveling wave systems are singular traveling wave systems of the second kind, which cannot have peakon solutions. Finally, an application example is presented to illustrate our theory and methodology using a model of nonlinear elastodynamics of materials with strong ellipticity.
报告人：李继彬
报告人简介：华侨大学和浙江师范大学特聘教授，博士生导师，动力系统与非线性研究中心负责人，国家级突出贡献专家, 1991年获首届国务院特殊津贴. 曾任四届国家自然科学基金委数学学科评审专家组成员, 三届云南省数学会理事长，云南省应用数学研究所副所长，昆明理工大学理学院院长等。 《应用数学与力学》等全国和国际性刊物的编委；美国《数学评论》与德国《数学文摘》评论员。主持承担国家自然科学基金重点项目和面上项目等10余项，发表论文350余篇，在“科学出版社”等出版中英文专著10余部，主编教材两部、出版科普书两本。三十余年培养硕士和博士研究生70余人. 科研成果曾分别获云南省和浙江省科学技术一等奖. 1987-2018年, 先后二十余次应邀到美国、俄国, 法国、加拿大、德国、英国、澳大利亚、西班牙、新加坡,南非等国家和香港, 澳门，台湾等地区多所大学和研究机构进行科研合作与学术交流。
时 间：2026年11月6日（周五）上午09:00-10:00
地 点：石牌校区南海楼124会议室
题目二：Some bifurcation results in near-Hamiltonian systems with finite-order smoothness
内容简介：This paper presents a systematic survey of bifurcation theory for near-Hamiltonian systems with finite-order smoothness. Unlike the classical C∞ or Cω framework, we collect some known results on limit cycle bifurcations for planar systems with finite-order smoothness, including Poincar´e bifurcation, Hopf bifurcation, homoclinic bifurcation, double homoclinic bifurcation, heteroclinic bifurcation, and bifurcations involving nilpotent singularities. For each type, we summarize the relevant bifurcation theorems on properties of the Melnikov functions and the conditions for the existence and the number of limit cycles that can be produced.
报告人：韩茂安
报告人简介：二级教授、博士生导师。于1987年6月在南京大学获得博士学位。曾被授予国家中青年突出贡献专家，获得教育部新世纪优秀教师支持计划，和宝钢优秀教师奖，自1992年起享受国务院政府特殊津贴。曾作为第一完成人分别获得教育部科技进步一等奖、上海市自然科学二等奖、上海市自然科学三等奖、上海市教学成果二等奖，已连续10次主持国家自然科学基金项目, 其中包括一项国家自然科学基金重点项目（2020-2024），已培养博士和博士后70多人，与合作者一起在国内外出版专著和教材10余部。2018年10月作为杰出教授任职于浙江师范大学。 长期从事常微分方程定性理论与动力系统分支理论的研究，在平面系统的定性研究与极限环分支、平面近哈密顿系统的极限环个数、周期微分方程的不变流形、非光滑系统的Melnikov 函数与平均法等多个方面建立了新理论，发表论文400多篇。作为主编分别在上海交大、上海师大与浙江师大等三所大学创办三家国际数学杂志，连续多年入选高被引学者榜单。
时 间：2026年11月6日（周五）上午10:00-11:00
地 点：石牌校区南海楼124会议室
题目三：Patterns and stability switches driven by the range of nonlocal effects and memory delay
内容简介：Motivated by the need to understand how spatial and temporal nonlocalities jointly shape ecological dynamics, this paper studies a memory-based diffusion equation with finite-range intraspecific competition and memory delay.
We reveal that the competition range governs the system's response to delay. For unbounded domains, two critical range thresholds delineate regimes where delay is inactive, triggers oscillations, or cannot restore stability. In bounded domains, the range alone induces multiple stability switches and spatial patterns; delay further generates inhomogeneous periodic and quasi-periodic solutions. We also demonstrate that domain boundedness uniquely enables stability switches absent in unbounded spaces. Biologically, these results explain how moderate nonlocal competition and memory drive population cycles, patterns, and traveling waves.
报告人：宋永利
报告人简介：杭州师范大学数学学院教授、博士生导师、教育部新世纪优秀人才、浙江省高等学校“钱江学者”特聘教授、中国生物数学会理事。 主要从事微分方程定性理论、无穷维动力系统的分支理论、斑图动力学的研究工作，取得了一系列高水平的研究成果，在动力系统领域的国际权威期刊SIAM J. Applied Dynamical Systems、Journal of Differential Equations、Journal of Nonlinear Science、Nonlinearity、Studies in Applied Mathematics、IEEE Transactions on Neural Networks and Learning Systems、Physica D等发表学术论文90余篇。2014年起连续多年入选中国高被引学者榜单(数学类)。2022年入选斯坦福大学发布的全球前2%顶尖科学家榜单。曾主持多项国家自然基金和省部级重点项目的研究工作。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”、“浙江省优秀数学教师”和“杭州师范大学优秀研究生导师”称号。研究成果获威海市科学技术一等奖和浙江省自然科学三等奖。
时 间：2026年11月6日（周五）上午11:00-12:00
地 点：石牌校区南海楼124会议室
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