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报告题目: Boundedness, gradient estimate, blow-up and exponential convergence in a two-species and two-stimuli chemotaxis system with/without loop
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报告题目: Boundedness, gradient estimate, blow-up and exponential convergence in a two-species and two-stimuli chemotaxis system with/without loop

报 告 人:向田 副教授 中国人民大学

照片:

邀请人:李善兵

报告时间:2020年7月6日(周一) 15:00-16:00

腾讯会议ID: 410 235 053

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,人民大学青年学者B岗; 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相关模型的研究,已在CVPDE, SIAP, JDE, Nonlinearity, JNS, EJAM等杂志上发表三十余篇论文(含一篇博士学位论文),被引用187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,博士后基金一等以及国家自然科学基金青年基金的资助。

报告摘要: In this talk, we report dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model with/without chemical signalling loop in a 2D bounded and smooth domain. In radial and elliptic simplification settings, we provide a substantial step toward the (simultaneous) global boundedness and (simultaneous) finite-time blow up. In the general case, i.e., no radial and elliptic simplifications, we successfully detect the product of two species masses as a feature to determine boundedness, gradient estimate, blow-up and W^{j,\infty}( j\geq 1)-exponential convergence of classical solutions for the corresponding IBVP. This report is based on recent two joint projects with K. Lin from Southwestern University of Finance and Economics.

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