学术报告报告主题: Boundary spike-layer solutions of the singular Keller-Segel system: existence, profiles and stability
报 告 人: 王治安 教授
报告时间：2025年 11月27日（星期四）下午15:30-16:30
报告地点：37号楼3A02
邀 请 人: 洪广益副教授
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数学学院
2025年11月24日
报告摘要：
This talk is concerned with the boundary-layer solutions of the singular Keller-Segel model in a multi-dimensional domain describing the chemotactic movement of cells up to the concentration gradient of the nutrient consumed by cells, where the zero-flux boundary condition is imposed to the cell while inhomogeneous Dirichlet boundary condition to the nutrient. The steady-state problem of the Keller-Segel system 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 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 as is nutrient diffusion coefficient small. Furthermore, we establish the nonlinear exponential stability of the boundary-layer steady-state solution for the radially symmetric domain.
报告人介绍：
王治安，香港理工大学应用数学系教授，华中师大本科硕士，加拿大艾伯塔大学应用数学博士，美国明尼苏达大学应用数学所博士后。主要从事与生物数学相关的偏微分方程建模及分析研究。目前已在Proc. London Math. Soc、J. London Math. Soc.、J. Math. Biol.、JMPA、CPDE、SIAM J. Math. Anal.、SIAM J. Appl. Math.、Indiana U. Math. J. 等杂志上发表学术论文100多篇。现担任杂志J. Mathematical Biology, DCDS-B，MBE等杂志编委。多次获得香港研究资助局基金资助以及2022年国家自然科学基金委-香港研究资助局联合基金资助。曾获香港数学会青年学者奖。