The Stability of Nontrivial Positive Steady States for the SKT Model with Large Cross Diffusion  

作　　者：Qing LI Qian XU 

机构地区：[1]College of Arts and Sciences,Shanghai Maritime University,Shanghai 201306,China [2]Institute of Fundamental and Interdisciplinary Sciences,Beijing Union University,Beijing 100101,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第3期657-669,共13页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11871048,No.11501031,No.11471221,No.11501016);Premium Funding Project for Academic Human Resources Development in Beijing Union University(BPHR2019CZ07,BPHR2020EZ01);Beijing Municipal Education Commission(KZ201310028030,KM202011417010)。

摘　　要：This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion.By applying the detailed spectral analysis and in virtue of the bifurcating direction to the limiting system as the cross diffusion rate tends to infinity,it is proved the stability/instability of the nontrivial positive steady states with some special bifurcating structure.Further,the existence and stability/instability of the corresponding nontrivial positive steady states for the original cross-diffusion system are proved by applying perturbation argument.

关 键 词：spectral analysis STABILITY cross-diffusion system 

分 类 号：O175.2[理学—数学]