应用数学系学术报告

--- 分析与偏微分方程讨论班(2023秋季第7讲)

On effects of the nonlinear signal production to the

boundedness and finite-time blow-up in a flux-limited

chemotaxis model

穆春来

（重庆大学数学与统计学院教授）

报告时间： 10：00-11：00，2023-10-17（星期二上午）

报告地点：  腾讯会议： 702-732-336

https://meeting.tencent.com/dm/90JokUo257hr

内容简介： This work deals with the initial-boundary value problem for the flux-limited chemotaxis model with nonlinear signal production

subject to no-flux boundary conditions in a ball

whereFor radially symmetric and positive initial data , it is proved that the corresponding solution is globally bounded when p > max{k, q}. This result not only fills up a gap left in (J. Differential Equations 267 (2019) 5115-5164, Acta. Appl. Math. 167 (2020) 231-259) when k = 1, but also extend the boundedness result from the special case k = 1 (Commun. Partial Differ. Equ. 42 (2017) 436-473) to the general case k > 0. Moreover, under the condition

it is shown that if c is sufficiently large, then there exists initial data such that the corresponding solution blows up at finite time T^* in the sense that

This blow-up result generalize the works for the linear signal production case in (Trans. Am. Math. Soc. Ser. B 4 (2017) 31-67, Acta. Appl. Math. 167 (2020) 231-259) to the nonlinear case k > 1.

报告人简介： 穆春来教授现任重庆大学数学与统计学院院长，博士生导师，中国数学会理事，重庆市数学会副理事长，主要从事非线性偏微分方程、生物数学和图像处理理论和应用研究。2005年入选“教育部新世纪优秀人才”计划，2008入选重庆市学术与技术带头人。先后承担了多项国家自然科学基金、教育部新世纪优秀人才基金、教育部优秀年轻教师基金、重庆市自然科学重点基金项目。2015年获得重庆市自然科学奖二等奖一项；2014年获得国家教学成果二等奖一项。已在“Math Mod Meth Appl. Sci”、“J. Diff. Equs”、“J. Nonlinear Sci.”、“Proc. Roy. Soc. Edingh Sec. A”、“Dis. Contin. Dyn. Syst.”、“Z. Angew. Math. Phys”等国内外重要数学期刊发表论文200余篇。

邀请人：郑孝信