微分方程与动力系统小型研讨会

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微分方程与动力系统小型研讨会

简历

王治安，香港理工大学应用数学系教授，加拿大艾伯塔大学应用数学博士，美国明尼苏达大学应用数学所博士后。主要从事与生物数学相关的偏微分方程建模及分析研究。目前已在J. Math. Pures Appl.、Proc. London Math. Soc.、J. London Math. Soc.、J. Math. Biol.、Comm. Partial Differential Equations、SIAM J. Math. Anal.、SIAM J. Appl. Math.、Indiana U. Math. J.等杂志上发表学术论文100多篇。现担任杂志J. Mathematical Biology, DCDS-B, MBE等杂志编委。多次获得香港研究资助局基金资助以及2022年国家自然科学基金委-香港研究资助局联合基金资助。曾获香港数学会青年学者奖。

报告题目

Nonlinear stability of traveling wave solutions to the Keller-Segel system with logistic source

报告

主要观点

Over the past decade, traveling wave solutions to chemotaxis models with logistic sources have been extensively investigated, whereas their stability remain largely unexplored. In this talk, we will present some first-hand findings on the nonlinear stability of traveling wave solutions for such chemotaxis models, which admit an explicit minimal wave speed. Our analysis covers both the critical and non-critical wave speed scenarios.

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简历

王毅,中国科技大学数学科学学院教授、博士生导师。2002年获得中国科技大学理学博士学位。曾应邀对美国佐治亚理工学院、芬兰赫尔辛基大学、美国明尼苏达大学IMA研究所长期学术访问，现任中国科大数学科学学院副院长。主要研究领域为微分方程与动力系统，先后在包括JEMS、 Adv. Math、 Proc. London Math. Soc.、SIAM J. Math. Anal.、JDE、Tans. Amer. Math. Soc.等国际杂志发表论文30余篇。2004年入选全国百篇优秀博士论文，2007年入选教育部新世纪优秀人才支持计划，国家级人才。

报告题目

单调动力系统---不变锥系统的发展与展望

报告

主要观点

本报告简要介绍单调动力系统 理论的历史、发展与展望。

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简历

方健，哈尔滨工业大学数学学院教授、副院长。2005年于大连理工大学本科毕业后，到哈尔滨工业大学攻读基础数学博士学位，2011年毕业后留校工作，2012年晋升教授。其间，2007至2010年在加拿大纽芬兰纪念大学学习，2011至2015年分别在加拿大约克大学和法国社会科学高等研究院做博士后研究。曾获全国优博提名和首届秦元勋青年数学奖，入选国家青年人才计划。主要从事扩散系统时空传播理论及应用研究，在JEMS, JMPA, MathAnn等期刊发表论文二十余篇。

报告题目

Bistable propagation dynamics for a degenerate reaction-diffusion system modeling Wolbachia's invasion

报告

主要观点

We study the propagation dynamics for a bistable delayed reaction-diffusion system with degeneracy in diffusion. This model is used to describe the population suppression of wild mosquitoes via releasing Wolbachia-infected mosquitoes. We first obtain the existence of bistable wave, which is then shown to have a unique speed. Such a uniqueness is then used to completely characterize the sign of this speed in terms of releasing size of mosquitoes. When the speed is positive, we further investigate the long term behavior of solutions starting from a family of ordered and compactly supported initial values; two thresholds for initial values are identified to distinguish the convergence of these solutions to different stable equilibria, and this corresponds to the success or failure of population suppression.

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简历

宋永利，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、Nonlinearity、Journal of Differential Equations、Journal of Nonlinear Science、SIAM J. Appl. Math、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年起连年入选中国高被引学者榜单（数学类）。2022年起连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科学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 “杭州市优秀研究生导师”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。

报告题目

Complex dynamics indued by the joint effect of nonlocal delay and diffusion

报告

主要观点

In this talk, the influence of the distributed delay (nonlocality in time) and nonlocal delay (nonlocality in space) on the stability and spatiotemporal dynamics in the memory-based diffusion populations are discussed. For the distributed delay, it has been shown that the weak kernel does not affect the stability of this positive constant steady state, but the strong kernel can lead to the rich dynamics. For the nonlocal delay, it has been shown that when movement driven by the memory-based diffusion is slow, the memory does not the stability of positive homogeneous steady state, but when the movement driven by the memory-based diffusion is fast, the small memory delay (no matter how small it is) can destabilize the stability, however the large memory can stabilize the stability. A series of Turing bifurcation, Hopf bifurcation, Turing-Turing bifurcation and double Hopf bifurcation are explicitly determined.

主讲人照片

简历

梁兴，中国科学技术大学教授，博士生导师，获得全国百篇优秀博士论文、中国数学会钟家庆数学奖、教育部新世纪优秀人才等多项国家级人才称号。主持多项国家自然科学基金项目。主要研究兴趣为抛物系统和扩散系统的时空动力学及相关问题，已在CPAM、JMPA、PLMS 、Adv. Math、Math Ann、TAMS、JFA、JDE等数学杂志发表学术论文多篇。工作被动力系统、偏微分方程、生物数学界同行广泛引用。

报告题目

Spreading Speeds for Fisher-KPP Equations with Slowly Decaying Initial Data in Almost Periodic Media

报告

主要观点

This work studies how far and fast beneficial genes (or invasive species) spread in one-dimensional media with almost periodic heterogeneity, when the initial population decays slowly at infinity.

For slowly fading initial data (e.g., algebraic or stretched-exponential tails), we prove the invasion front accelerates beyond the classical linear speed. The front location is governed by the inverse of the initial decay profile, scaled by a spectral constant from the linearized operator.

We develop a tail-adapted Hamilton-Jacobi framework to unify:

? classical linear-speed spreading for compact/exponential tails,

? accelerated propagation for slow tails,

? almost periodic media where standard periodic homogenization fails.

Our results extend prior periodic/random media theories and provide quantitative predictions for biological invasions in complex environments.

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