On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains

被引:40
作者
Cantrell, Robert Stephen [1 ]
Cosner, Chris [1 ]
机构
[1] Univ Miami, Dept Math, Coral Gables, FL 33124 USA
基金
美国国家科学基金会;
关键词
reaction-diffusion; logistic equation; nonlinear boundary conditions; Allee effect; eigenvalue problems; bifurcation;
D O I
10.1016/j.jde.2006.08.018
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study a diffusive logistic equation with nonlinear boundary conditions. The equation arises as a model for a population that grows logistically inside a patch and crosses the patch boundary at a rate that depends on the population density. Specifically, the rate at which the population crosses the boundary is assumed to decrease as the density of the population increases. The model is motivated by empirical work on the Glanville fritillary butterfly. We derive local and global bifurcation results which show that the model can have multiple equilibria and in some parameter ranges can support Allee effects. The analysis leads to eigenvalue problems with nonstandard boundary conditions. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码:768 / 804
页数:37
相关论文
共 16 条
[1]  
ALEXANDER JC, 1981, ARCH RATION MECH AN, V76, P339
[2]  
Amann H., 1990, DIFFERENTIAL INTEGRA, V3, P13
[3]  
ANTRELL RS, 2003, SPATIAL ECOLOGY VIA
[4]  
Bandle C., 1980, ISOPERIMETRIC INEQUA
[5]   Conditional persistence in logistic models via nonlinear diffusion [J].
Cantrell, RS ;
Cosner, C .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2002, 132 :267-281
[6]  
CANTRELL RS, IN PRESS B MATH BIOL
[7]  
Courant R., 1953, METHODS MATH PHYS, V1
[8]  
CRANDALL MG, 1973, ARCH RATION MECH AN, V52, P161, DOI 10.1007/BF00282325
[9]   Allee effect and population dynamics in the Glanville fritillary butterfly [J].
Kuussaari, M ;
Saccheri, I ;
Camara, M ;
Hanski, I .
OIKOS, 1998, 82 (02) :384-392
[10]  
Ladyzhenskaya O., 1968, LINEAR QUASILINEAR E, DOI DOI 10.1090/MMONO/023