学术报告

题      目： On a Keller--Segel System of Chemotaxis with Signal-dependent Motility

报  告  人：江杰   副研究员  (邀请人：王勇 )

                                 中国科学院精密测量科学与技术创新研究院

时      间：2022-06-21 15:00-17:00

腾 讯 会 议 ：535-148-760（无密码）

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。2004年毕业于山东大学数学与系统科学学院基地班，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CPDE、CVPDE、JDE、SIMA等国际数学刊物正式发表SCI论文27篇。曾主持国家自然科学基金、湖北省自然科学基金各一项。

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), and Yanyan Zhang (ECNU).