Phase separation and free boundary problems for aggregation-diffusion phenomena
数学专题报告
报告题目(Title)：Phase separation and free boundary problems for aggregation-diffusion phenomena
报告人(Speaker)：Antoine Mellet (University of Maryland)
地点(Place)：Zoom ID: 991 1148 4217, PWD: 600657
时间(Time)：2025 年 3月 28日 9：30-10：30
邀请人(Inviter)：熊金钢
报告摘要
We investigate phase separation phenomena that arise as a result of the competition between nonlocal attraction and local repulsion in classical aggregation-diffusion models (we will mainly discuss the Patlak-Keller-Segel model). We will present some recent results showing that when a large population of organisms is observed at some appropriate scales (in time and space), a sharp interface appears, separating regions of high and low density. The derivation of free boundary problems to describe the motion of this interface shows that the collective dynamics is driven, at macroscopic scales, by surface tension and contact angle phenomena as in classical models of fluid dynamics.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
