【11月19日上午】陈秀卿 教授:Global Existence and Uniqueness analysis of Reaction-Cross-Diffusion Systems

讲座时间 Datetime: 
星期一, 2018/11/19 - 08:3010:00
地点 Venue: 
海滨红楼6号楼1楼会议室
报告人 Speaker: 
陈秀卿 教授
单位 Affiliation: 
北京邮电大学
报告摘要 Abstract: 

The global-in-time existence of weak and renormalized solutions to reaction-cross-diffusion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions are proved. The cross-diffusion part describes the segregation of population species and is a generalization of the Shigesada-Kawasaki-Teramoto model. The diffusion matrix is not diagonal and generally neither symmetric nor positive semi-definite, but the system possesses a formal gradient-flow or entropy structure. The reaction part is of Lotka-Volterra type for weak solutions or includes reversible reactions of mass-action kinetics and does not obey any growth condition for renormalized solutions. Furthermore, we prove the uniqueness of bounded weak solutions to a special class of cross-diffusion systems, and the weak-strong uniqueness of renormalized solutions to the general reaction-cross-diffusion cases.