LIMITING CHARACTERIZATION OF STATIONARY SOLUTIONS FOR A PREY-PREDATOR MODEL WITH NONLINEAR DIFFUSION OF FRACTIONAL TYPE

被引：0

作者：

Kuto, Kousuke ^{[1
]}

Yamada, Yoshio ^{[2
]}

机构：

[1] Fukuoka Inst Technol, Dept Intelligent Mech Engn, Higashi Ku, Fukuoka 8110295, Japan

[2] Waseda Univ, Dept Appl Math, Shinjuku Ku, Tokyo 1698555, Japan

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2009年 / 22卷 / 7-8期

基金：

日本学术振兴会;

关键词：

POSITIVE SOLUTIONS; STEADY-STATES; BIFURCATION; EQUATIONS; STABILITY; PAIRS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following quasilinear elliptic system: {Delta u + u(a - u - cv) = 0 in Omega, Delta[(1 + gamma/1+beta u)v] + v(b + du - v) = 0 in Omega, u = v = 0 on partial derivative Omega, where Omega is a bounded domain in R-N. This system is a stationary problem of a prey-predator model with non-linear diffusion Delta(v/1 + beta u) and u (respectively v) denotes the population density of the prey (respectively the predator). Kuto [15] has studied this system for large beta under the restriction b > (1 + gamma)lambda(1), where lambda(1) is the least eigenvalue of -Delta with homogeneous Dirichlet boundary condition. The present paper studies two shadow systems and gives the complete limiting characterization of positive solutions as beta -> infinity without any restriction on b.

引用

页码：725 / 752

页数：28

共 24 条

[1] DYNAMIC THEORY OF QUASILINEAR PARABOLIC EQUATIONS .1. ABSTRACT EVOLUTION-EQUATIONS [J].