报告人简介：向田，中国人民大学副教授。研究方向：偏微分方程。已发表期刊论文29篇，MR引用117次。

报告摘要：We study chemotaxis effect (chi) vs logistic damping(mu) on boundedness (and large time behavior) for the minimal Keller-Segelmodel with logistic source in 2- and 3-D smooth and bounded domains. We obtainqualitative boundedness on chi and mu: up to a scaling constant depending onlyon initial data and the underlying domain, we provide explicit upper bounds forthe L-infinity norm of solution components of the correspondinginitial-boundary value problem.Thesebounds are increasing in chi and decreasing in mu.

In 2-D, the corresponding upper bounds have only onesingularity in mu at mu=0. In contrast, in 3-D, the upper bounds, holding undera critical explicit relation between chi and mu (which has been shown toguarantee boundedness ), are defined for all chi and mu>const. chi, and,have two singularities in muatmu=0 and mu=const. chi.It is worthwhile to mention that, in theabsence of logistic source, the corresponding classical KS model is well-knownto possess blow-ups for even small initial data. We hope that these qualitativefindings presented here would produce some new principles on finite-timeblow-up to chemotaxis systems with weak logistic damping sources.

报告主持：陶有山 教授