论文标题
使用几何形状降低的Fisher-kpp-burgers系统中的推动正面
Pushed fronts in a Fisher-KPP-Burgers system using geometric desingularization
论文作者
论文摘要
我们在一个由反应性流动问题动机的一维反应扩散方程的系统中研究旅行前线。在限制中作为参数倾向于无穷大，我们构造了近似的前轮廓，并确定所选波动的领先顺序扩展。这样的前部通常被构造为稳定和不稳定的流动波差分方程的横向交叉点。但是，对因变量的重新缩放导致缺乏终端状态之一的双曲线，从而使某人的定义不清楚。我们使用几何爆破技术来恢复双曲线，然后在对吹动的向量场进行分析之后，能够显示出具有其速度领先阶段的行进前线的存在。
We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine the leading order expansion for the selected wavespeed. Such fronts are often constructed as transverse intersections of stable and unstable manifolds of the traveling wave differential equation. However, a re-scaling of the dependent variable leads to a lack of hyperbolicity for one of the end states making the definition of one such manifold unclear. We use geometric blow-up techniques to recover hyperbolicity and following an analysis of the blown up vector field are able to show the existence of a traveling front with a leading order expansion of its speed.
