对于具有时空时滞的一维反应扩散系统中波前解的存在性,已有文献利用单调迭代技术结合适当的上下解和非标准排序的方法来证明.由于物种一般生存在高维的环境中,文章将这些方法推广到二维空间上,证明具有非局部效应的二维反应扩散方程波前解的存在性.
Abstract
For the existence of travelling wave fronts of one-dimensional reaction-diffusion systems with spatio-temporal delays, the monotone iteration technique coupled with the upper-lower solutions and nonstandard ordering methods has been used to prove it. Since species generally exist in high-dimensional environments, this paper extends these methods to two-dimensional space and proves the existence of travelling wave fronts of two-dimensional reaction-diffusion systems with nonlocal effects.
关键词
二维反应扩散方程 /
非局部效应 /
波前解
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Key words
two-dimensional reaction-diffusion systems /
nonlocal effect /
travelling wave fronts
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参考文献
[1] MURRAY J D. Mathematical biology: I.An introduction[M].3rd. New York: Springer,2002.
[2] BRITTON N F. Aggregation and the competitive exclusion principle[J]. Journal of Theoretical Biology,1989,136:57-66.
[3] BRITTON N F. Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model[J]. SIAM Journal on Applied Mathematics, 1990, 50(6): 1663-1688.
[4] CHEN S, YU J. Stability and bifurcations in a nonlocal delayed reaction-diffusion population model[J]. Journal of Differential Equations, 2016, 260(1): 218-240.
[5] WANG Z C, LI W T, RUAN S. Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays[J]. Journal of Differential Equations, 2006, 222(1): 185-232.
[6] 程翠平.二维格上单种群模型的传播速度和行波解[D].兰州:兰州大学,2007.
[7] 程翠平.二维格上具有年龄结构单种群模型的行波解[D].兰州:兰州大学,2010.
[8] 史振霞.二维格上年龄结构单种群模型双稳行波解[D].兰州:兰州大学,2008.
[9] 谈小莉,史振霞.二维格上单种群模型行波解的唯一性[J].兰州交通大学学报,2017,36(3):127-130.
[10]赵海琴.二维格上时滞微分方程的行波解[J].咸阳师范学院学报,2010,25(4):10-12.
[11]LAN K, WU J. Travelling wave fronts of reaction-diffusion equations with and without delays[J]. Nonlinear Analysis: Real World Applications,2003,4:173-188.
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脚注
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