报告题目: Reaction-Advection-Diffusion Parabolic Systems Modeling Chemotaxis
报 告 人：向田 副教授 （中国人民大学数学科学研究院）
In first part of the talk, we are concerned with a class of Keller-Segel chemotaxis systems with cross-diffusion, in which we especially focus on the cross-diffusion effects on the qualitative behaviors of the systems including global existence, pattern formations and asymptotic behavior etc. In particular, we use the entropy method to establish a global existence of weak solutions with the effects of cross diffusion included in ≤3-D and identify two cross-diffusion ratesδcand δc: the first one distinguishes the possibility of pattern formations and the second one distinguishes the stability of the emerging patterns.
In the second part, we study a general class of parabolic KS chemotaxis systems with growth sources. It is recently known that blowup is possible even in the presence of superlinear growth restrictions. Here, we first derive several characterizations on the growth versus boundedness. Then we apply these criteria to the minimal KS model with a logistic source and obtain a quantitative description of the competition between chemotactic aggregation and logistic damping, and, in particular, establish how precisely strong a logistic source can prevent blow-up. Besides, it also gives a clue on how to produce blowup solutions for Keller-Segel chemotaxis models with logistic sources. Finally, we obtain an explicit relationship between chemotactic aggregation and logistic damping so that convergences are ensured and their respective convergence rates are explicitly calculated out.
Dr. Xiang, Tian received his PhD in Applied Mathematics at Tulane University (USA) in May 2014. From October 2014-August 2016, he works in the Institute For Mathematical Sciences at Renmin Universit