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题目: Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model

报告人：向田 副教授(中国人民大学)

报告时间：2020年12月25日下午3:00-4:00 (北京时间)

报告地点：沙河主楼 E602

摘要: In this talk, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a chemotaxis-haptotaxis model in 2D settings. It is well-known that the corresponding Keller-Segel chemotaxis-only model  possesses a striking feature of critical mass blowup phenomenon, namely, subcritical mass  ensures boundedness, whereas, supercritical mass induces the existence of blow-ups. Herein, we show that this critical mass blow-up phenomenon stays almost the same in the full chemotaxis-haptotaxis model and that any global-in-time haptotaxis solution component vanishes exponentially and the other two solution components converge exponentially to that of chemotaxis-only model in a global sense for suitably large chemo-sensitivity and in the usual sense for suitably small chemo-sensitivity. Therefore, haptotaixs is neither good nor bad than chemotaxis, showing negligibility of haptotaxis effect in the underlying chemotaxis-haptotaxis model.

报告人简介：向田，2014年5月博士毕业于美国杜兰大学（Tulane University），偏微分方程专业，现为人民大学数学科学研究院副教授，硕士生导师，曾获得2018人民大学杰出学者青年B岗以及2019人民大学优秀论文成果奖; 研究兴趣为偏微分方程及其应用， 非线性分析以及动力系统，近年来主要从事趋化交错相关模型的研究， 已在CVPDE, SIAP, JDE, Nonlinearity, JNS, EJAM, JMP，DCDS等杂志上发表三十篇论文，被引用近300余次(mathscinet)，研究获得中央高校科研启动基金，人民大学人才培育基金，博士后基金一等，国家自然科学基金青年以及面上基金的资助。

邀请人：郑孝信