报告题目： The effect of density-suppressed motility in a Keller--Segel system of chemotaxis

报告人：江杰 副研究员 中国科学院精密测量科学与技术创新研究院

报告时间：2021年7月12日（星期一） 10:50-11:40

报告地点：海山楼 B1410

校内联系人：禹芳                  联系电话：84708351-8096

报告摘要：In this talk, we would like to report our recent work on a Keller—Segel system of chemotaxis, featuring a density-suppressed motility. This model was originally proposed by Keller and Segel in their seminal work in 1971, which models the cellular movements due to a local sensing chemotaxis. An extended model was also developed in some recent works of Biophysics to study the process of pattern formation, involving a density-suppressed motility, which stands for a repressive effect of the signal on cell motility.

From a mathematical point of view, the model features a signal-dependent motility, which may vanish as the concentration becomes unbounded, leading to a possible degenerate problem. Conventional energy methods can only deal with some special cases and the existence of classical solutions with generic motility functions is a long standing open problem. Recently, we develop a new comparison method based on the nonlinear structure which provides us an explicit point-wise upper bound estimate for the concentration. Then, we study the global existence of classical solutions and discuss their boundedness in any dimensions. 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).

报告人简介：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，目前正式发表SCI论文18篇。 曾主持国家自然科学基金一项。