报告题目：A nonlocal cross-diffusion model for interaction of scroungers with foragers

报告人：陶有山（上海交通大学，教授）

报告时间：2022年11月3日 14：00-16：30

报告地点：腾讯会议ID：743-899-818

校内联系人：王金环

报告摘要：As a simplified version of a three-component taxis-cascaded model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. We shall discuss the global existence, boundedness as well as stabilization of a global classical solution to the corresponding no-flux initial-boundary value problem. This is a joint work with Michael Winkler (Paderborn). 

报告题目：Maximum principle of strong solutions of the non-divergence parabolic equations

报告人：王明新（河南理工大学，教授）

报告时间：2022年11月3日 14：00-16：30

报告地点：腾讯会议ID：743-899-818

校内联系人：王金环

报告摘要：It is well-know that the upper and lower solution method is based on the comparison principle, and the comparison principle is based on the maximum principle. In view of the limitation of compatibility conditions, the Schauder theory can not be directly used in the upper and lower solution methods, but the L ^ p theory. Therefore, the maximum principle of strong solutions becomes the basis of the upper and lower solution method. For divergence parabolic equation, the maximum principle of strong solutions can be proved by using the integration method. However, for the non-divergence parabolic equation, the integral method cannot be used, and other methods are needed. In this talk, the maximum principle of strong solution for non-divergence parabolic equation is proved by using smooth approximation.