论文标题
在单稳定方程的推动波前，单峰延迟反应
On pushed wavefronts of monostable equation with unimodal delayed reaction
论文作者
论文摘要
我们研究了Mackey-Glass型单稳定延迟反应扩散方程，并具有单峰出生功能$ g（u）$。该模型旨在描述单个物种种群的演变，在存在弱质量效应的情况下（$ g（u_0）> g'（0）u_0 $，对于某些$ u_0> 0 $）。我们将注意力集中在缓慢的单调旅行方面的存在上：在给定的假设下，这个问题似乎很困难，因为通常的阳性和单调性论点无效。首先，我们解决了小延迟的前面存在问题，$ h \ in [0，h_p] $，其中$ h_p $（在某种意义上，$ h_p $（由显式公式给出）是最佳的。然后，我们采用代表性的线性单峰出生功能，从而可以对行进前线进行明确计算。在这种情况下，我们发现a）延迟的增加会破坏渐近稳定的推动前线； b）所有可允许的波前速度的集合具有半无限间隔$ [c_*， +\ infty）$的常规结构; c）对于每个$ h \ geq 0 $，推动的波前是唯一的（如果存在）； d）推动波可以在正平衡周围缓慢振荡，以获得足够的大延迟。
We study the Mackey-Glass type monostable delayed reaction-diffusion equation with a unimodal birth function $g(u)$. This model, designed to describe evolution of single species populations, is considered here in the presence of the weak Allee effect ($g(u_0)>g'(0)u_0$ for some $u_0>0$). We focus our attention on the existence of slow monotonic traveling fronts to the equation: under given assumptions, this problem seems to be rather difficult since the usual positivity and monotonicity arguments are not effective. First, we solve the front existence problem for small delays, $h \in [0,h_p]$, where $h_p$ (given by an explicit formula) is optimal in a certain sense. Then we take a representative piece-wise linear unimodal birth function making possible explicit computation of traveling fronts. In this case, we find out that a) increase of delay can destroy asymptotically stable pushed fronts; b) the set of all admissible wavefront speeds has usual structure of a semi-infinite interval $[c_*, +\infty)$; c) for each $h\geq 0$, the pushed wavefront is unique (if it exists); d) pushed wave can oscillate slowly around the positive equilibrium for sufficiently large delays.
