一般反应扩散Stefan模型中的紧支行波
Compactly supported travelling waves arising in a general reaction-diffusion Stefan model
摘要：
我们研究行波解的反应扩散方程，$\partial_t u= R(u) + \partial_x \left[D(u) \partial_x u\right]$，与Stefan一样的条件，在边缘的移动前。通过对$R(u)$和$D(u)$的一些假设，在反应扩散Stefan模型中产生了一系列新的紧支行波.虽然其他的反应扩散模型承认companies支持行波的一个独特的波速，我们表明，companies支持行波的反应扩散Stefan模型中存在的范围内的波速。此外，我们确定的必要条件$R(u)$和$D(u)$的紧支行波存在的所有波速。利用渐近分析在各种不同的限制的波速，我们得到这些行波的近似解，同意与数值模拟的高精度。
英文摘要：
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.
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