报告题目 (Title)：The Effect of Signal-dependent Motility in a Keller--Segel System of Chemotaxis(信号依赖性运动在Keller-Segel趋化系统中的作用)

报告人 (Speaker)：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 (Time)：2022年9月25日（周日）9:00

报告地点 (Place)：腾讯会议（ID：881-381-446 会议密码：6789）

邀请人(Inviter)：朱佩成

主办部门：理学院数学系

报告摘要：

In this talk, we would like to report our recent work on a Keller—Segel system of chemotaxis involving signal-dependent motility. This model was originally proposed by Keller and Segel in their seminal work in 1971, and has been used to provide a new mechanism for pattern formation in some recent Bio-physics work published in Science and PRL.

From a mathematical point of view, the model features a non-increasing signal-dependent motility function, which may vanish as the concentration becomes unbounded, leading to a possible degenerate problem. 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. Moreover, new iteration as well as monotonicity techniques are developed to study the global existence of classical solutions and their boundedness in any dimension. It is shown that the dynamic of solutions is closely related to the decay rate of the motility function at infinity. In particular, a critical mass phenomenon as well as an infinite-time blowup was verified in the two-dimensional case if the motility is a negative exponential function.

The talk is based on my recent joint works with Kentarou Fujie (Tohoku University), Philippe Laurençot (University of Toulouse and CNRS), Yanyan Zhang (ECNU), and Yamin Xiao (IAPCM).