The existence and stability of traveling waves with transition layers for the S-K-T competition model with cross-diffusion  

作　　者：Wu YaPing Zhao Ye 

机构地区：[1]Capital Normal Univ, Dept Math, Beijing 100048, Peoples R China [2]Beijing Inst Petrochem Technol, Dept Math & Phys, Beijing 102617, Peoples R China

出　　处：《Science China Mathematics》2010年第5期124-147,共24页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10671131);Beijing Natural Science Foundation (Grant No.1092006)

摘　　要：This paper is concerned with the existence and stability of traveling waves with transition layers for a quasi-linear competition system with cross diffusion,which was first proposed by Shegesada,Kawasaki and Teramoto.When one of the random diffusion rates is small and the cross-diffusion rate is not small,by the geometric singular perturbation method,the existence of traveling waves with transition layers is obtained.Further,by the detailed spectral analysis and topological index method,the traveling waves with transition layers are proved to be locally exponentially stable with shift.This paper is concerned with the existence and stability of traveling waves with transition layers for a quasi-linear competition system with cross diffusion,which was first proposed by Shegesada,Kawasaki and Teramoto.When one of the random diffusion rates is small and the cross-diffusion rate is not small,by the geometric singular perturbation method,the existence of traveling waves with transition layers is obtained.Further,by the detailed spectral analysis and topological index method,the traveling waves with transition layers are proved to be locally exponentially stable with shift.

关 键 词：TRAVELING waves EXISTENCE STABILITY CROSS-DIFFUSION spectral analysis UNSTABLE BUNDLE 

分 类 号：N[自然科学总论]