一个三维三角形交叉扩散系统的整体弱解

Global Weak Solutions in a Three-Dimensional Triangular Cross-Diffusion System

研究一个带交叉扩散的两物种竞争模型,其中一个物种带有交叉扩散但缺少自扩散。由于该模型在三维空间情形下的整体经典解的存在性至今仍是未知的,因此利用一种新的正则化方法,通过引入一个变量变换及运用先验估计技巧,构造出该三维模型的整体弱解。此弱解可以用正则化问题的经典解来逼近。

This paper studies a two-species competing model with cross-diffusion but without self-diffusion for one species.Since the global existence of classical solutions to this model is still unknown in the threedimensional case,the work constructs a global weak solution to the model based on a new regularizing approach and a transformation of variable as well as a priori estimate techniques.This weak solution can be approximated by classical solutions of regularized problems.