*主持人：何小清 教授

*讲座内容简介：

In this talk, we mainly study non-negative classical solutions to a Neumann initial-boundary value problem for a higher dimensional parabolic elliptic ODE minimal chemotaxis-haptotaxis system. We first show pure haptotaixs cannot induce any blow-up and pattern in any dimensions, showing negligibility of haptotaxis on boundedness. Then, in the radial setting, it is well-known that small mass of cells can lead to blow-up in the corresponding Keller-Segel chemotaxis-only model, known as generic mass blow-up phenomenon. Herein, in the presence of the temporal nonlocality brought by haptotaxis, we show, in an explicit realm, that the aforementioned generic mass finite time blow-up phenomenon preserves. This seems to be the first rigorous blow-up result in relevant chemotaxis-haptotaxis models. The blow-up result also suggests that haptotatic cross-diffusion may not be negligible compared to chemotactic aggregation in three or higher D, in contrast to the recently detected 2D negligibility of haptotaxis in a minimal chemotaxis haptotaxis model.

*主讲人简介：

向田，2014年5月博士毕业于美国杜兰大学（Tulane University），现为中国人民大学数学科学研究院/数学学院教授，博士生导师。 研究兴趣为偏微分方程及非线性分析,近年来主要关注趋化交错扩散方程组解的有界性,爆破性以及定性刻画等，已在M3AS, CVPDE, SIAP, JNS, JDE, Non-linearity, EJAM等杂志上发表论文三十余篇，被引用500余次(mathscinet)，多篇论文多次ESI高被引；曾获2020年北京市数学竞赛优秀指导老师，主持完成中央高校科研启动基金，人民大学人才培育基金，博士后一等基金以及国自科青年基金，目前主持一项国自科面上项目。