论文标题
以截止反应速率的KPP反应扩散模型中行进波的演变。 ii。行进波的演变
The Evolution of Travelling Waves in a KPP Reaction-Diffusion Model with cut-off Reaction Rate. II. Evolution of Travelling Waves
论文作者
论文摘要
在这一系列论文的第二部分中，我们考虑了Kolmogorov-Petrovskii-Piscounov（KPP）类型方程的初始值问题，并在浓度$ u = u_c $的反应函数中不连续截止。对于固定的截止值$ u_c \ in（0,1）$，我们应用了匹配的渐近坐标膨胀的方法，以获得完整的大型渐近形式的溶液，该溶液表现出了永久形式的波动波结构。特别是，这种方法允许对溶液到永久形式的波动速度的校正和通过小空间中的渐近结构进行详细分析来确定永久形式的行进波。针对截止Fisher反应函数的特定情况获得的数值结果证实了渐近结果。
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.
