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一类时滞反应扩散方程的行波解

Traveling Wave Fronts of a Class of Reaction-Diffusion Systems with Delay
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摘要 通过定义上下解和构造单调迭代序列,讨论在反应项是在弱拟单调的条件下,具有双时滞和超前反应扩散方程波前解的存在性. Existence of traveling wave front of reaction-diffusion systems with two delays and anticipation is obtained by defining the upper and lower solutions and constructing iteration equations when the reaction term satisfies the nonquasi-monotonicity condition.
作者 武红艳
机构地区 晋中学院数学学院
出处 《晋中学院学报》 2016年第3期6-10,共5页 Journal of Jinzhong University
关键词 具有时滞和超前反应扩散方程 行波解 上下解方法 单调迭代技术 reaction diffusion systems with retardation and anticipation traveling wave front upper and lower solutions monotone iterative technique
分类号 O175.1 [理学—基础数学]
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参考文献7

  • 1Wu Jianhong, Zou Xingfu. Traveling wave fronts of reaction-diffusion stems with delay [ J ]. Dynamic Differential Equations, 2001, 13 : 651 ~687.
  • 2Wu Jianhong, Zou Xingfu. Existence of traveling wave fronts in delayed reaction-diffusion systems via the monotone iteration method [J]. Proc.Amer.Math.Soc, 1997, 125:2589-2598.
  • 3Ma Siwang. Traveling wave fronts for delayed reaction-diffusion systems via a fixed point theorem [J ]. J. Differential Equations, 2001, 171:294-314.
  • 4Wang Zaicheng, Li Wantong, Ruan Shigui. Existence and stability of traveling wave fronts in reaction advection diffusion equations ~ith nonlocal delay [J ]. J. Differential Equations, 2007, 238:153-200.
  • 5Chern I-Liang, Meiming. Stability of non-monotone critical traveling waves for reaction-diffusion equations with time-delay [J]. J. Differential Equations, 2015,3.
  • 6Yao Meiping, Zhao Aimin, Yan Jurang. Monotone method for first order functional differential equations with retardation and anticipation [J ]. Nonlinear Analysis, 2009, 71 : 4223-4230.
  • 7武红艳.一类捕食与被捕食模型的行波解[J].太原师范学院学报（自然科学版）,2011,10(4):17-19. 被引量：2

二级参考文献4

  • 1Wu J ,Zou X. Existence of traveling wave fronts in delayed reaction-diffusion systems via the monotone iteration method[J]. Proc. Amer. Math. Soc. ,1997,125:2 589-2 598.
  • 2Boumenir A, Minh N V. Perron theorem in the monotone iteration method fortraveling waves in delayed reaction-diffusion equations. [J]. J. Differential Equations, 2008,244 : 1 551-1 570.
  • 3Wu J,Zou X. Traveling wave fronts of reaction-diffusion systems with delay[J]. Dynamics Differential Equations, 2001,13: 651-687.
  • 4H uang J, Lu G, Ruan. Existence of traveling wave solutions in a diffusive predator-prey model[J]. J. Math. Biol, 2003 (4) : 132- 152.

共引文献1

晋中学院学报
2016年 第3期

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