报告题目：Chemotactic aggregation vs logistic damping in the minimal Keller-Segel model
报告摘要：We study chemotaxis effect (chi) vs logistic damping (mu) on boundedness (and large time behavior) for the minimal Keller-Segel model with logistic source in 2- and 3-D smooth and bounded domains. We obtain qualitative boundedness on chi and mu: up to a scaling constant depending only on initial data and the underlying domain, we provide explicit upper bounds for the L-infinity norm of solution components of the corresponding initial-boundary value problem. These bounds are increasing in chi and decreasing in mu.
In 2-D, the corresponding upper bounds have only one singularity in mu at mu=0. In contrast, in 3-D, the upper bounds, holding under a critical explicit relation between chi and mu (which has been shown to guarantee boundedness ), are defined for all chi and mu>const. chi, and, have two singularities in mu at mu=0 and mu=const. chi. It is worthwhile to mention that, in the absence of logistic source, the corresponding classical KS model is well-known to possess blow-ups for even small initial data. We hope that these qualitative findings presented here would produce some new principles on finite-time blow-up to chemotaxis systems with weak logistic damping sources.
报告人概况：向田，中国人民大学副教授。他的主要研究兴趣为非线性偏微分方程及其应用， 非线性分析以及动力系统；已在SIAM JAM, JDE, Nonlinearity, JNS, EJAM, DCDS等杂志上发表近三十篇论文，为多个杂志审稿以及在第8届ICIAM以及第12届AIMS国际会议上组织过两个分组研讨会；研究得到中央高校科研启动基金，人民大学人才培育基金，博士后基金一等以及国家自然科学基金青年基金的资助。