Title: On global solutions and blow-up for a short-ranged chemicalsignaling loop
Reporter: XIANG Tian (Renmin University of China)
Time: May 31, 2019 (Thursday) PM 15:00-16:00
Location: A1101# room, Innovation Park Building
Contact: CAO Yang
Abstract: In this talk, we consider the global boundedness and blow-up of solutions to a two-species and two-stimulus chemotaxis model, in which the process of the species results in a short-ranged chemical signaling loop. Explicit conditions on the initial data are given for the simultaneous global boundedness and simultaneous finite-time blow up of classical solutions. More precisely, since the dynamic of one species are expected to be essentially determined by the other through this chemotactic signaling loop between two cell types, we find that smallness of mass of each species implies global solvability, whereas, largeness of masses induce blow-up to occur. These in particular improve the known existing knowledge where smallness of total masses of both two species is required. This is a joint work with K. Lin from Southwestern University of Finance and Economics.
The brief introduction to the reporter: Xiangtan, Ph. D. graduated from Tulane University in May 2014. He is an associate professor at Renmin University and a young scholar at Renmin University. He has been a tutor of master's degree since 2018. His main research interests are non-linear partial differential equations and their applications, non-linear analysis and dynamic systems; he has published nearly 30 papers in SIAM JAM, JDE, Nonlinearity, JNS, EJAM, DCDS, JMP and other magazines; his research has been funded by the Central University Research Initiation Fund, Renmin University Talents Cultivation Fund, Post-doctoral Fund and the National Natural Science Foundation Youth Fund.