應yl7703永利官網(wǎng)李萬同教授與孫建文副教授邀請，美國奧本大學沈文仙教授將于2022年6月24日-6月26日與我校有關師生進行在線學術研討，其中6月26日舉行線上專題學術報告。

報告題目:Finite-time blow-up prevention by logistic source in parabolic-elliptic chemotaxis models with singular sensitivity in any dimensional setting

時 間：6月26日上午10:00

騰訊會議ID： 79018627942 密碼： 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.

沈文仙教授簡介

沈文仙教授1987年于北京大學數(shù)學系獲得碩士學位；1992年于美國喬治亞理工學院數(shù)學學院獲得博士學位。自1992于美國奧本大學數(shù)學系任教，2002后成為全職教授。沈教授多年來致力于研究許多微分方程中的動力學問題，包括異質和隨機介質理論中的行波解，單調動力系統(tǒng)中的Lyapunov指數(shù)理論，非局部擴散算子的譜理論及應用，和擬周期反應擴散方程的漸近動力學行為。沈教授在《Transactions of The American Mathematical Society》、《Journal of Differential Equations》、《Journal ofDynamics and Differential Equations》等國際著名期刊上發(fā)表學術論文80余篇，論文被引用超過1000多次，主持過多項國家自然科學基金。

甘肅應用數(shù)學中心

甘肅省高校應用數(shù)學與復雜系統(tǒng)省級重點實驗室

yl7703永利官網(wǎng)

萃英學院

2022年6月22日