SOME MONOTONE PROPERTIES FOR SOLUTIONS TO A REACTION-DIFFUSION MODEL

被引:12
作者
Li, Rui [1 ]
Lou, Yuan [2 ]
机构
[1] Renmin Univ China, Inst Math Sci, Beijing 100876, Peoples R China
[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
来源
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 08期
关键词
Reaction-diffusion; steady state; diffusion rate; monotone property; SPATIAL HETEROGENEITY; DISPERSAL; EQUATIONS; DYNAMICS; SINGLE;
D O I
10.3934/dcdsb.2019126
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Motivated by the recent investigation of a predator-prey model in heterogeneous environments [20], we show that the maximum of the unique positive solution of the scalar equation {mu Delta theta + (m(x) - theta)theta = 0 in Omega, partial derivative theta/partial derivative n = 0 on partial derivative Omega (0,1) is a strictly monotone decreasing function of the diffusion rate it for several classes of function m, which substantially improves a result in [20]. However, the minimum of the positive solution of (0.1) is not always monotone increasing in the diffusion rate [15].
引用
收藏
页码:4445 / 4455
页数:11
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