Speaker: Jiang Jie, associate research fellow, Innovation Academy for Precision Measurement Science and Technology, CAS

Date: November. 12, 2021

Time: 13:30-14:30

Location: Tencent Meeting, ID: 766 643 340

Sponsor: School of Mathematics, Shandong University

Abstract:

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).

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/159030.htm