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具有时滞和超前反应扩散方程的行波解 被引量：1

Traveling Wave Fronts of Reaction Diffusion Systems with Retardation and Anticipation
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摘要 现在时滞反应扩散方程行波解的研究越来越广泛,但是同时具有时滞和超前的反应扩散方程结果却很少.文章通过定义上下解和构造单调迭代序列,在反应项是拟单调的条件下,得到了具有双时滞和超前反应扩散方程波前解的存在性. Many results about traveling wave fronts of reaction-diffusion systems with de lay are obtained, but traveling wave fronts of reaction diffusion systems with retardation and an ticipation are hardly considered. Existence of traveling wave front is obtained by defining the up per and lower solutions and constructing monotone iteration equations when the reaction term sat isfies the quasi-monotonicity condition.
作者 武红艳
机构地区 晋中学院数学学院
出处 《太原师范学院学报（自然科学版）》 2015年第4期12-13,17,共3页 Journal of Taiyuan Normal University:Natural Science Edition
关键词 具有时滞和超前的反应扩散方程 行波解 上下解方法 单调迭代技术 reaction diffusion systems with retardation and anticipation~ traveling wavefront upper and lower solutions monotone iterative technique
分类号 O175.14 [理学—基础数学]
  • 相关文献

参考文献7

  • 1WU Jianhong, ZOU Xingfu. Existence of traveling wave fronts in delayed reaction-diffusion systems via the monotone iteration methodrJ']. Proc. Amer. Math. Soc, 1997,125:2589-2598.
  • 2WU Jianhong,ZOU Xingfu. Traveling wave fronts of reaction-diffusion stems with delay[J]. Dynamic Differential Equations, 2001,13:651-687.
  • 3MA Siwang. Traveling wave fronts for delayed reaction-diffusion systems via a fixed point Theorem[J]. J. Differentia[ Equa tions, 2001,171 : 294-314.
  • 4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
  • 5WANG Zaicheng,LI Wantong,RUAN Shigui. Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delayl-J']. J. Differential Equations,2007,238:153-200.
  • 6CHERN I Liang, Meiming. Stability of non-monotone critical traveling waves for reaction diffusion equations with time-delay [J]. J. Differential Equations,2015(3).
  • 7YAO Meiping,ZHAO Aimin,YAN J urang. Monotone method for first order functional differential equations with retardation and anticipation[J]. Nonlinear Analysis, 2009,71 : 4223-4230.

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

同被引文献5

  • 1WU Jianhong,ZOU Xingfu. Traveling wave fronts of reaction-diffusion stems with delay [J]. Dynamic Differential Equations, 2001,13 : 651-687.
  • 2MA Siwang. Traveling wave fronts for delayed reaction-diffusion systems via a fixed point theorem[J]. J. Differential Equa-tions, 2001,171:294-314.
  • 3WANG Zaicheng,LI Wantong,RUAN Shigui. Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay[J]. J. Differential Equations, 2007,238 : 153-200.
  • 4CHERN I Liang, MEI ming,YANG Xiangfeng. Stability of non-monotone critical traveling waves for reaction-diffusion equa- tions with time delay[J]. J. Differential Equations,2015,259:1503-1541.
  • 5YAO Meiping,ZHAO Aimin,YAN Jurang. Monotone method for first order functional differential equations with retardation and anticipation[J]. Nonlinear Analysis, 2009,71 : 4223-4230.

引证文献1

二级引证文献2

太原师范学院学报（自然科学版）
2015年 第4期

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