报告题目：Boundary spike-layer solutions to the multi-dimensional singular Keller-Segel model
报告人：李敬宇 教授 东北师范大学
报告时间：2025年5月22日 13:30-14:30
报告地点：数学楼第一报告厅
校内联系人：刘长春 liucc@jlu.edu.cn
报告摘要：
We are interested in the boundary-layer solutions to the singular Keller-Segel model in a multi-dimensional domain describing the bacteria consuming nutrient, where the bacteria satisfies zero-flux boundary condition and the nutrient satisfies inhomogeneous Dirichlet boundary condition. The steady-state problem is reduced to a scalar Dirichlet nonlocal elliptic problem with singularity. Studying this nonlocal problem, we obtain the unique steady-state solution which possesses a boundary spike-layer profile as the nutrient diffusion coefficient tends to zero. When the domain is radially symmetric, we find the explicit expansion for the slope of boundary-layer profiles at the boundary and boundary-layer thickness in terms of the radius. Furthermore, we establish the nonlinear exponential stability of the boundary-layer steady-state solution for the radially symmetric domain. This is a joint work with J. Carrillo, Zhi-An Wang and Wen Yang.
报告人简介：
李敬宇教授，东北师范大学数学与统计学院教授，博士生导师，主要研究生物趋化方程及流体力学方程中的稳定性与不稳定性现象；在Proc. London Math. Soc., SIAM J. Math. Anal., Math. Models Methods Appl. Sci., J. Differential Equations等高水平杂志上发表几十篇论文，多次获得国家自然科学基金面上项目和省部级项目的资助。
