報告題目：Global boundedness and stabilization in a two-competing-species chemotaxis-fluid system with two chemicals

報告人：穆春來（教授）

報告時間：2020年7月21日（星期二）16：00-17：30

報告地點：明理樓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.

報告人簡介：

穆春來，重慶大學數學與統計學院院長，教授，博士導師。2005年入選“教育部新世紀優秀人才”計劃，2008入選重慶市學術與技術帶頭人。先后承擔了多項國家自然科學基金、教育部新世紀優秀人才基金、教育部優秀年輕教師基金、重慶市自然科學重點基金項目。2015年獲得重慶市自然科學獎二等獎一項；2014年獲得國家教學成果二等獎一項。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”等國內外重要數學期刊發表論文200余篇。

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