Travelling Waves and Numerical Approximations in a Reaction Advection Diffusion Equation with Nonlocal Delayed Effects
Travelling Waves and Numerical Approximations in a Reaction Advection Diffusion Equation with Nonlocal Delayed Effects
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DOI：
10.1007/s00332-003-0524-6
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发表时间：
2003-06
影响因子：
3
通讯作者：
D. Liang;Jianhong Wu
中科院分区：
文献类型：
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作者：
D. Liang;Jianhong Wu
在本文中，我们考虑了生活在空间运输场中具有两个年龄段和固定成熟期的单一物种种群的增长动态。如果成熟死亡率和扩散率与年龄无关，则可导出具有时间延迟和非局部效应的反应平流扩散方程 (RADE) 模型。我们讨论了著名的尼科尔森吹蝇方程中出现的具有三个出生函数的延迟模型行波的存在性，并考虑和分析了非局域时滞效应问题的波动方程中行波前的数值解。特别是，我们报告了有关单调性变化和多峰波可能出现的数值观测结果。通过计算具有非局部延迟的全时变偏微分方程，在数值上考虑了行波波前的稳定性。
In this paper, we consider the growth dynamics of a single-species population with two age classes and a fixed maturation period living in a spatial transport field. A Reaction Advection Diffusion Equation (RADE) model with time delay and nonlocal effect is derived if the mature death and diffusion rates are age independent. We discuss the existence of travelling waves for the delay model with three birth functions which appeared in the well-known Nicholson's blowflies equation, and we consider and analyze numerical solutions of the travelling wavefronts from the wave equations for the problems with nonlocal temporally delayed effects. In particular, we report our numerical observations about the change of the monotonicity and the possible occurrence of multihump waves. The stability of the travelling wavefront is numerically considered by computing the full time-dependent partial differential equations with nonlocal delay.