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Chemotaxis aggregation vs logistic damping in the minimal Keller-Segel model


Academic Report

Title: Chemotaxis aggregation vs logistic damping in the minimal Keller-Segel model

Reporter: XIANG Tian (Renmin University of China)

Time: May 17, 2018 (Thursday) AM 9:30-10:30

Location: A1101# room, Innovation Park Building

Contact: A.Prof. DAI Guowei (tel:84708351-8135)

Abstract: 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.

The brief introduction to the reporter: He graduated from Tulane University in partial differential equations in May 2014 and became a postdoc in the Institute of Mathematical Science of Renmin University of China from September 2014 to August 2016. Then he was an associate professor of Renmin University of China in September 2016 and a master's tutor in 2018. His main research fields are nonlinear partial differential equations and its applications, nonlinear analysis and dynamical systems. He has published more than twenty papers in magazines such as JDE and Nonlinearity and organized a seminar on the eighth ICIAM. And his research has been funded by the Central University Research initial funding, the postdoctoral fund and the Youth Foundation of National Natural Science Fund.