Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Di
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Di
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DOI：
10.1016/j.jde.2007.03.025
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发表时间：
2007-07
影响因子：
2.4
通讯作者：
Zhi-Cheng Wang;Wan-Tong Li;S. Ruan;W.-T Li
中科院分区：
文献类型：
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作者：
Zhi-Cheng Wang;Wan-Tong Li;S. Ruan;W.-T Li
本文研究了具有非局域时滞的准单调反应平流扩散方程中行波前的存在性、唯一性和全局渐近稳定性。在双稳态假设下，我们构造了各种超解和子解对，并利用比较原理和压缩技术证明了该方程具有唯一的非递减行波前（直到平移），该波前单调递增且具有相移全局渐近稳定。还考虑了平流对传播速度的影响。与之前的结果相比，我们的结果恢复和/或改进了许多现有的结果。特别是，这些结果可以应用于具有非局部延迟效应的反应平流扩散方程和具有分布式成熟延迟的扩散群体模型，得到了一些新的结果。
This paper is concerned with the existence, uniqueness and globally asymptotic stability of traveling wave fronts in the quasi-monotone reaction advection diffusion equations with nonlocal delay. Under bistable assumption, we construct various pairs of super- and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front (up to translation), which is monotonically increasing and globally asymptotically stable with phase shift. The influence of advection on the propagation speed is also considered. Comparing with the previous results, our results recovers and/or improves a number of existing ones. In particular, these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay, some new results are obtained.