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陈秀卿 12月15日下午2点 腾讯会议:621551104 Global Existence and Uniqueness analysis of Reaction-Cross-Diffusion Systems

报告题目:Global Existence and Uniqueness analysis of Reaction-Cross-Diffusion Systems

报告时间:1215日下午2

报告地点:腾讯会议:621551104

报告人:陈秀卿,中山大学

报告人简介:

 

  陈秀卿, 中山大学“百人计划”教授,博士生导师,中国工业与应用数学会理事。研究方向为偏微分方程。已经在Commun. Math. Phys., Arch. Rational Mech. Anal., SIAM J. Math. Anal., J. Differential EquationsM3AS等国际知名学术期刊上发表论文二十多篇。主持完成和在研国家自然科学基金面上项目各一项。20113月至20122月公派访问杜克大学。先后于20131月至20136月,20175月至20184月,分别作为访问教授或访问学者,在维也纳工业大学进行合作研究。

  

报告简介

    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.