应304am永利集团官网李万同教授与孙建文副教授邀请，美国奥本大学沈文仙教授将于2022年6月24日-6月26日与我校有关师生进行在线学术研讨，其中6月26日举行线上专题学术报告。

报告题目:Finite-time blow-up prevention by logistic source in parabolic-elliptic chemotaxis models with singular sensitivity in any dimensional setting

时 间：6月26日上午10:00

腾讯会议ID： 79018627942 密码： 123456

摘 要：In recent years, it has been drawn a lot of attention to the question of whether logistic kinetics is sufficient to enforce the global existence of classical solutions or to prevent finite-time blow-up in various chemotaxis models. However, for several important chemotaxis models, only in the space two-dimensional setting, it has been shown that logistic kinetics is sufficient to enforce the global existence of classical solutions. In this talk, we give a confirmed answer to the above question for parabolic-elliptic chemotaxis models with singular sensitivity and logistic source in any space dimensional setting. We prove that, for every given nonnegative initial data, such a system has a unique globally defined classical solution, which shows that, in any space dimensional setting, logistic kinetics is sufficient to enforce the global existence of classical solutions and hence prevents the occurrence of finite-timeblow-up even for arbitrarilylarge chemotaxis sensitivity. We also show that the $L^p$-norm of any globally defined positive solution is bounded without anyassumption on the parameters in the model. In addition, if the logistic growth rate is not small relative to the chemotaxis sensitivity, we show that any globally defined positive solution is bounded above and below eventually by some positive constants independent of its initial functions.

沈文仙教授简介

沈文仙教授1987年于北京大学数学系获得硕士学位；1992年于美国乔治亚理工学院数学学院获得博士学位。自1992于美国奥本大学数学系任教，2002后成为全职教授。沈教授多年来致力于研究许多微分方程中的动力学问题，包括异质和随机介质理论中的行波解，单调动力系统中的Lyapunov指数理论，非局部扩散算子的谱理论及应用，和拟周期反应扩散方程的渐近动力学行为。沈教授在《Transactions of The American Mathematical Society》、《Journal of Differential Equations》、《Journal ofDynamics and Differential Equations》等国际著名期刊上发表学术论文80余篇，论文被引用超过1000多次，主持过多项国家自然科学基金。

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

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2022年6月22日