Effect of cross-diffusion in the diffusion prey-predator model with a protection zone II

被引：20

作者：

Li, Shanbing ^{[1
]}

Yamada, Yoshio ^{[2
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China

[2] Waseda Univ, Dept Math Sci, Tokyo 1698555, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 461卷 / 01期

基金：

日本学术振兴会;

关键词：

Cross-diffusion; Protection zone; Coexistence solution; Limiting behavior; Shadow system; COMPETITION MODEL; NONLINEAR DIFFUSION; STATIONARY PROBLEM; BIFURCATION; SYSTEM;

D O I：

10.1016/j.jmaa.2017.12.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the current paper, we continue the mathematical analysis studied in Li and Wu (2017) [15] and Oeda (2011) [22], and further study the effect of cross-diffusion for the predator on the stationary problem. The existence of positive solutions is first established by the bifurcation theory. We next discuss the limiting behavior of positive solutions when the intrinsic growth rate of the predator species tends to infinity. Moreover, as the prevention coefficient tends to infinity, we obtain two shadow systems and give the complete limiting characterization of positive solutions. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：971 / 992

页数：22

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