具有交叉扩散的相互竞争生态系统的上下解方法

On the Method of Upper and Lower Solutions for the Competition Ecological Model with Cross-diffusion

文章的目的是研究一类具有交叉扩散的相互竞争椭圆生态系统,其方程是强耦合的,且系数允许间断。利用上下解方法和相关的单调迭代,在适当的假设条件下,得到了正逐片古典解的存在性。这种方法还为以后数值解的计算提供了构造过程。

The aim of this paper is to investigate an elliptic competition ecological system with crossdiffusion.This system is strongly coupled and the coefficients of the equations are allowed to be discontinuous.By the method of upper and lower solutions and its associated monotone iterations,the existence of positive piecewise classical solutions is obtained under certain conditions.This approach leads to a constructive procedure for the solution which is potentially useful for the computation of numerical solutions.