Positive solutions for Lotka–Volterra competition system with large cross-diffusion in a spatially heterogeneous environment. (August 2017)

• Record Type: Journal Article
• Authors: Li, Shanbing; Liu, Sanyang; Wu, Jianhua; Dong, Yaying
• Is Part Of: Nonlinear analysis. Volume 36(2017)
• Page Start: 1
• Page End: 19
• Publication Date: 2017-08
• Subjects: Cross-diffusion -- Bifurcation -- Asymptotic behaviour -- Blow up; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.12.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the stationary problem for the Lotka–Volterra competition system with cross-diffusion in a spatially heterogeneous environment. Although some sufficient conditions for the existence of positive solutions are obtained by using global bifurcation theory, the information for their structure is far from complete. In order to get better understanding of the competition system with cross-diffusion, we focus on the asymptotic behaviour of positive solutions and derive two shadow systems as the cross-diffusion coefficient tends to infinity, moreover, the structure of positive solutions of the limiting system is analysed. The result of asymptotic behaviour also reveals different phenomena from that studied in Wang and Li (2013).