Traveling waves in nonlocal diffusion systems with delays and partial quasi-monotonicity

被引：0
作者：
Zhao-quan Xu
Pei-xuan Weng
机构：
[1] South China Normal University,Department of Mathematics
来源：
Applied Mathematics-A Journal of Chinese Universities | 2011年 / 26卷
关键词：
Traveling wave; nonlocal diffusion; partial quasi-monotonicity; upper and lower solution; cross iteration scheme; 34K25; 35K57; 92D25.;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.
引用
收藏
页码：464 / 482
页数：18
相关论文
共 50 条
  • [11] Chmaj A.(2010)Traveling waves of a three-species Lotka-Volterra foodchain model with spatial diffusion and time delays Nonlinear Analysis RWA 11 2817-2832
  • [12] Coville J.(2006)Travelling wave solutions in delayed reaction diffusion systems with partial monotonicity Acta Mathematicae Applicatae Sinica, English series 22 243-256
  • [13] Dupaigne L.(2005)Traveling wave solutions in delayed lattice differential equations with partial monotonicity Nonlinear Analysis TMA 60 1331-1350
  • [14] Coville J.(2006)Existence of traveling solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems Nonlinearity 19 1253-1273
  • [15] Dupaigne L.(2009)Traveling wave solutions in diffusive and competition-cooperation systems with delays IMA J Applied Mathematics 74 604-621
  • [16] Coville J.(2010)Traveling wave solutions in delayed reaction diffusion systems with applications t o multi-species models Discrete and Continuous Dynamical Systems B 13 393-414
  • [17] Dupaigne L.(2001)Traveling wavefronts for delayed reaction-diffusion systems via some fixed point theorems J Differential Equations 171 294-314
  • [18] Ermentrout B.(2009)Traveling wave fronts in delayed diffusion systems via a cross iteration scheme Nonlinear Analysis RWA 10 2807-2818
  • [19] Mcleod J.(2009)Traveling wave fronts in nonlocal delayed reaction-diffusion systems and applications Z Angew Math Phys 60 377-392
  • [20] Gilpin M.(1987)Asymptotic behavior and traveling wave solutions for parabolic functional differential equations Trans Amer Math Soc 302 587-615
12345