Global Existence and Uniqueness analysis of Reaction-Cross-Diffusion Systems

讲座时间 Datetime: 

星期一, 2018/11/19 - 从 08:30 到 10:00

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.