报告题目1：Sharp viscous shock waves for relaxation model with degeneracy

报告人：梅茗教授，加拿大麦吉尔大学及Champlain学院

报告时间：2025年6月28日（周六）13:30-17:30

报告地点：20-200

报告摘要：This talk is concerned with a relaxation model with degeneracy. Different from the existing studies on the regular viscous shock waves, we recognize that, when the sub-characteristic condition is degenerate, the dynamical system possesses sharp viscous shock waves, a new type of viscous shock waves with sharp corners and being regionally degenerate in a half space. The regularities of these sharp viscous shock waves are further derived. Some of them can be smooth due to different degree of degeneracy, but most of them are Hölder continuous with sharp corners. The exact sharp viscous shock waves are constructed for three typical equations, and the corresponding numerical simulations with given initial data are also presented, which perfectly match the exact sharp viscous shock waves, and also numerically demonstrate the stability of sharp shock waves. This is a joint work with Shufang Xu, Wancheng Shen, and Zejia Wang.

报告人简介：梅茗，加拿大麦吉尔大学Adjunct Professor，加拿大尚布兰学院终身教授，江西师范大学特聘教授，国家基金委外国资深学者，科技部海外高端人才，日本文部省JSPS外国资深学者，国际学术机构ScholarGPS发布的2024全球顶尖科学家排名前0.98%。主要从事Navier-Stokes方程、欧拉方程、欧拉-泊松方程、时滞反应扩散方程解的定性分析等方面的研究，在ARMA, SIMA, M3AS等一流学术刊物发表论文140 余篇，被《美国数学评论》列为SIMA及JDE的top authors，有4篇论文是ESI高被引论文。是《Applicable Analysis》等4个SCI国际期刊的编委，也一直是“科学探索奖”评审专家之一。

报告题目2：Self-similar singular solution of Keller-Segel  model with signal consumption

报告人：金春花教授，华南师范大学

报告时间：2025年6月28日（周六）13:30-17:30

报告地点：20-200

报告摘要：In this talk, we investigates the finite-time blow-up phenomenon in a Keller-Segel model with signal consumption and singular sensitivity. We establish the existence of backward self-similar solutions, demonstrating chemotactic collapse where bacteria concentrate into a Dirac $\delta$-measure while oxygen vanishes completely at the blow-up time. Notably, this occurs for any initial mass size.  The results provide insights into bacterial aggregation mechanisms under limited oxygen conditions.

报告人简介：金春花，华南师范大学，教授。长期从事非线性扩散模型相关理论的研究，研究工作发表在Bull. London Math. Soc., J Nonlinear Sci., Nonlinearity，Physica D, JDE，JDDE 等期刊。入选教育部新世纪优秀人才支持计划，广东省特支计划-青年拔尖人才，主持包括国家自然科学基金面上项目等在内的多项研究课题。

报告题目3：Global existence, boundedness, and stabilization for a three-component reaction-diffusion model with dual-dependent motility

报告人：金海洋教授，华南理工大学

报告时间：2025年6月28日（周六）13:30-17:30

报告地点：20-200

报告摘要：In this talk, we address an initial-boundary value problem for a three-component reaction-diffusion system where the random motility response function depends on both chemical concentration and nutrient levels. Using the comparison method, we first prove the global existence of classical solutions in any spatial dimension for generic positive, non-increasing motility functions that vanish at infinity. Furthermore, in two-dimensional settings, we establish global boundedness and asymptotic stabilization of solutions for two distinct chemical signal generation mechanisms.

报告人简介：金海洋，华南理工大学数学学院教授，博士生导师。2011-2014就读于香港理工大学应用数学系并获得博士学位。目前研究方向主要集中在生物趋向性运动的相关理论及其应用。近年来在SIMA, SIAP, JNS, M3AS, JDE, Nonlinearity等期刊发表SCI论文30余篇, 2022年以第一完成人获广东省自然科学二等奖一项，现主持国家自然科学基金项目面上项目等。

报告题目4：Existence and nonexistence of stable patterns in semilinear nonlocal diffusion equations

报告人：李芳教授，中山大学

报告时间：2025年6月28日（周六）13:30-17:30

报告地点：20-200

报告摘要：In this talk, we consider the dynamics of semilinear nonlocal diffusion equations on bounded domains with no-flux boundary conditions, specifically focusing on the existence and stability of non-constant steady states, referred to as patterns. According to the results of  Casten, Holland, and Matano regarding semilinear local diffusion equations, we know that stable patterns do not exist in convex domains, while they do emerge in dumbbell-shaped geometries, particularly when the kinetic term is bistable. We extend these findings to nonlocal diffusion analogs, demonstrating the absence of stable smooth patterns in both one-dimensional intervals and multi-dimensional balls. In addition, we construct discontinuous, asymptotically stable patterns when the kinetic term is bistable. Our results reveal a significant principle: large nonlocal diffusion tends to destabilize patterns, whereas weak nonlocal diffusion stabilizes them, especially in cases with bistable kinetic terms. Importantly, the geometry of the domain appears to play a less critical role in this process of stabilization. This is joint work with Xueli Bai and Xuefeng Wang.

报告人简介：李芳，本科毕业于浙江大学，博士毕业于美国明尼苏达大学。现在中山大学数学学院工作，教授，博士生导师。主要研究非线性椭圆和抛物方程(组)。这些方程(组)涉及生物、化学、材料等很多科学领域。近年来，关注反应扩散方程中的非局部效应等相关问题。主持多项国家自然科学基金项目、省部级自然科学基金项目，曾参与国家自然科学基金重点项目和数学天元基金重点专项。研究成果发表在J. Math. Pures Appl., J. Funct. Anal., Calc. Var. PDE，Indiana Univ. Math. J.等国际数学期刊上。

报告题目5：Removable singularities and unbounded asymptotic profiles of multi-dimensional Burgers equations

报告人：季善明教授，华南理工大学

报告时间：2025年6月28日（周六）13:30-17:30

报告地点：20-200

报告摘要：This talk is concerned with the unbounded radially symmetric profiles and their asymptotic stability of the multi-dimensional Burgers equations on the whole space. The possible singularities near the origin of the unbounded stationary solutions are investigated and we show that both the convection and the diffusion have singularities in the sense of distributions for three dimensional Burgers equations, such that their singularities cancel with each other in the Burgers equations. We present the decay estimates of perturbations for unbounded solutions around the singular profile with large perturbations.

报告人简介：季善明，男，华南理工大学数学学院副教授、硕士生导师、TCL青年学者。主要研究方向为非线性偏微分方程。在Mathematische Annalen、SIAM Journal on Mathematical Analysis、Journal of Nonlinear Science、Calculus of Variations and Partial Differential Equations、Nonlinearity、Journal of Differential Equations等杂志上共发表SCI论文30余篇。承担国家自然科学基金面上项目、青年基金、广东省自然科学基金、广州市基础与应用基础研究项目等多项科研项目。

邀请人：无限维动力系统和偏微分方程研究所