Global boundedness and stabilization in a two-competing-species chemotaxis-fluid system with two chemicals

报告题目：Global boundedness and stabilization in a two-competing-species chemotaxis-fluid system with two chemicals

报告人：穆春来（教授）

报告时间：2020年7月21日（星期二）16：00-17：30

报告地点：明理楼C302b

摘要：This talk deals with a two-competing-species chemotaxis-fluid system with two different signals in a liquid surrounding environment and a smooth bounded domain. Firstly, when N=2 and κ=1, based on the standard heat-semigroup argument, it is proved that for all appropriately regular nonnegative initial data and any positive parameters, this system possesses a unique global bounded solution. Secondly, when N=3 and κ=0, by using the maximal Sobolev regularity and semigroup technique, it is proved that the system admits a unique globally bounded classical solution provided that there exists θ_0 > 0 such that max{χ_1,χ_2}/min{μ_1,μ_2}< θ_0. Finally, by means of energy functional and comparison arguments, it is shown that the global bounded solution of the system converges to different constant steady states, according to the different values of a_1 and a_2. Furthermore, we give the precise convergence rates of global solutions. Joint work with Pan Zheng and Robert Willie.

报告人简介：

穆春来，重庆大学数学与统计学院院长，教授，博士导师。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. EdinghSec. 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。

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