一、题目

On a Keller--Segel System of Chemotaxis with Density-suppressed Motility

二、主讲人

江杰

三、摘要

In this talk, we would like to report our recent work on a Keller—Segel system of chemotaxis, featuring density-suppressed motility, which was originally proposed by Keller and Segel in their seminal work in 1971. From a mathematical point of view, the model features signal-dependent motility, which may vanish as the concentration becomes unbounded, leading to a possible degenerate problem. Recently, we develop systematic new methods to study the well-posedness problem. The key idea lies in an introduction of an elliptic auxiliary problem which enables us to apply delicate comparison arguments to derive the upper bound of concentration. Then, we study the global existence of classical solutions and discuss their boundedness in any dimension. In particular, a critical mass phenomenon as well as an infinite-time blowup was verified in the two-dimensional case. The talk is based on my recent joint works with Kentarou Fujie (Tohoku University), Philippe Laurençot (University of Toulouse and CNRS), and Yanyan Zhang (ECNU).

四、主讲人介绍

江杰，中国科学院精密测量科学与技术创新研究院副研究员，2009年于复旦大学数学科学学院获得理学博士学位，师从郑宋穆教授。2009年到2011年在北京应用物理与计算数学研究所郭柏灵院士指导下从事博士后工作。主要针对多类非线性发展方程，如相场-流体方程组、趋化方程组等，考察整体解的存在唯一性、有界性、渐近性、平衡态以及无穷维动力系统的性质等，目前在SIMA、CVPDE、JDE等国际数学刊物正式发表SCI论文25篇。曾主持国家自然科学基金、湖北省自然科学基金各一项

五、邀请人

陈章 数学学院教授

六、时间

11月12日（周五）13:30-14:30

七、地点

腾讯会议，会议ID：766 643 340

八、主办方

山东大学数学学院