数学与统计及交叉学科前沿论坛------高端学术讲座第114场

报告题目：Starting-point Entropy and Shigesada–Kawasaki–Teramoto Model

报告人：陈秀卿教授 中山大学

时间：2024年7月12日（周五）16:00-17:00

地点：阜成路校区综合楼1116

参加对象：新葡萄8883官网AMG全体教师及研究生

报告人简介：陈秀卿，中山大学“百人计划”教授，博士生导师，数学学院（珠海）副院长，中国工业与应用数学会第七届理事。研究方向为偏微分方程。在CMP、ARMA、SIMA等学术期刊上发表论文三十多篇。先后主持国家自然科学基金多项。

报告摘要：The existence of global weak solutions to the cross-diffusion model of Shigesada, Kawasaki, and Teramoto for an arbitrary number of species is proved. The model consists of strongly coupled parabolic equations for the population densities in a bounded domain with no-flux boundary conditions, and it describes the dynamics of the segregation of the population species. The diffusion matrix is neither symmetric nor positive semidefinite. A new logarithmic entropy allows for an improved condition on the coefficients of heavily nonsymmetric diffusion matrices, without imposing the detailed-balance condition that is often assumed in the literature. Furthermore, the large-time convergence of the solutions to the constant steady state is proved by using the relative entropy associated to the logarithmic entropy.