报告题目：Global solvability, regularity and exponential convergence in a quasilinear chemotaxis haptotaxis system with mostly repulsive signal production

报告人：向田教授

时间：4月9日周四15:30-16:30

地点：腾讯会议 864-543-916

摘要：Motivated from biological and mathematical viewpoints, we systematically study global dynamics in a quasilinear chemotaxis haptotaxis system with mostly repulsive signal production. For a wide range of hapto-sensitivies, we establish uniform boundedness and exponential convergence of classical solutions to its constant equilibrium. Next, for a class of models including the minimal chemotaxis-haptotaxis model, we establish uniform boundedness and exponential convergence of classical solutions under suitable smallness conditions on initial data in optimal Lebesgue spaces irrespective of the sign of chemo-coefficient, which extends and improves related existing results. Finally, for the physical dimension three, under reasonable growth condition on hapto-sensitivity, we first show global existence of weak solutions, and then, we show intermediate and eventual regularity and exponential convergence of the derived global weak solutions. These findings greatly extend the well-known knowledge on the corresponding repulsive chemotaxis-only model to the repulsive chemotaxis-haptotaxis model, showing positive effect of chemo-repulsion on global dynamics in such chemotaxis haptotaxis settings.

向田：2014年博士毕业于美国杜兰大学，现为中国人民大学数学学院教授，博导。研究兴趣为偏微分方程及其应用，近年来主要关注趋化交错扩散模型解的有界性，爆破性以及定性行为等，发表论文40余篇，部分结果发表在CVPDE, JDE,M3AS, SAM, SIAP等杂志上，被引用900余次(mathscinet)。曾获2024年全国大学生数学竞赛优秀指导教师等；主持完成一项博士后基金，一项国家自然科学基金青年项目及一项国家自然科学基金面上项目。