In Part II of this series of papers, we consider an initial-boundary value problem for the Kolmogorov--Petrovskii--Piscounov (KPP) type equation with a discontinuous cut-off in the reaction function at concentration $u=u_c$. For fixed cut-off value $u_c \in (0,1)$, we apply the method of matched asymptotic coordinate expansions to obtain the complete large-time asymptotic form of the solution which exhibits the formation of a permanent form travelling wave structure. In particular, this approach allows the correction to the wave speed and the rate of convergence of the solution onto the permanent form travelling wave to be determined via a detailed analysis of the asymptotic structures in small-time and, subsequently, in large-space. The asymptotic results are confirmed against numerical results obtained for the particular case of a cut-off Fisher reaction function.

中文翻译：

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具有截止反应速率的 KPP 反应扩散模型中行波的演化。二、行波的演变

在本系列论文的第二部分，我们考虑了 Kolmogorov--Petrovskii--Piscounov (KPP) 型方程的初始边界值问题，在浓度 $u=u_c$ 时反应函数具有不连续截断。对于固定的截止值 $u_c \in (0,1)$，我们应用匹配渐近坐标展开的方法来获得解的完整大时间渐近形式，该形式表现出永久形式行波结构的形成。特别是，这种方法允许通过对小时间和随后大空间中的渐近结构的详细分析来确定对波速的修正以及解决方案在永久形式行波上的收敛率。