学术报告

报告题目： Chemotaxis aggregation vs logistic damping in the minimal Keller-Segel model

报告时间：2018年5月17日（周四）9：30－10：30

报告地点：创新园大厦A1101报告厅

报告人：向田  (中国人民大学)

校内联系人：代国伟， 电话：84708351-8135

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 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.

报告人简介：向田，2014年5月博士毕业于Tulane University，偏微分方程专业，2014年9月至2016年8月在中国人民大学数学科学研究院做博士后，2016年9月起为中国人民大学副教授， 2018年起为硕士生导师。向田副教授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JDE, Nonlinearity等杂志上发表二十余篇论文，在第8届ICIAM上组织过一个研讨会。 其研究得到中央高校科研启动基金，博士后基金一等以及国家自然科学基金青年基金的资助。