论文标题
在一般反应扩散Stefan模型中产生的紧凑支撑的行驶波
Compactly supported travelling waves arising in a general reaction-diffusion Stefan model
论文作者
论文摘要
我们检查了反应扩散方程的行进波解，$ \ partial_t u = r（u） + \ partial_x \ left [d（u）\ partial_x u \ right] $，在移动前部的边缘具有stefan样条件。在$ r（u）$和$ d（u）$上只有几个假设，在此反应扩散Stefan模型中出现了各种新的紧凑型行进波。虽然其他反应扩散模型接收了一个独特的波动的紧凑型行驶波，但我们表明反应扩散Stefan模型中紧凑的支持行驶波在一系列波动范围内存在。此外，我们确定了$ r（u）$和$ d（u）$的必要条件，这些条件均为所有波动的紧凑型行驶波。在波动的各种杰出范围内，使用渐近分析，我们获得了这些行进波的近似解，同意具有高精度的数值模拟。
We examine travelling wave solutions of the reaction-diffusion equation, $\partial_t u= R(u) + \partial_x \left[D(u) \partial_x u\right]$, with a Stefan-like condition at the edge of the moving front. With only a few assumptions on $R(u)$ and $D(u)$, a variety of new compactly supported travelling waves arise in this Reaction-Diffusion Stefan model. While other reaction-diffusion models admit compactly supported travelling waves for a unique wavespeed, we show that compactly supported travelling waves in the Reaction-Diffusion Stefan model exist over a range of wavespeeds. Furthermore, we determine the necessary conditions on $R(u)$ and $D(u)$ for which compactly supported travelling waves exist for all wavespeeds. Using asymptotic analysis in various distinguished limits of the wavespeed, we obtain approximate solutions of these travelling waves, agreeing with numerical simulations with high accuracy.
