论文标题
在自由接口问题中的存在，并存在分数阶动力学的界面问题
Existence of a traveling wave solution in a free interface problem with fractional order kinetics
论文作者
论文摘要
在本文中，我们考虑了两个反应扩散方程的系统，该系统将扩散 - 热燃烧模拟使用逐步点火 - 温度动力学和分数反应顺序0 <$α$ <1。我们将自由界面问题转变为标量的自由边界问题，并与积分方程相连。主要的中介步骤是将标量问题减少到维度2中非C 1矢量场的研究。后者通过基于Poincar {é} -Bendixson定理的定性托托逻辑方法来处理后者。确定了阶段肖像，并证明了起源处的稳定流形的存在。一个重要的结果是，到达原点的沉降时间是有限的，这意味着与$α$ = 1的情况相反，尾随界面是有限的，但按照$α$ = 0。最后，通过固定点方法求解了整数差异化系统。
In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 < $α$ < 1. We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-C 1 vector field in dimension 2. The latter is treated by qualitative topo-logical methods based on the Poincar{é}-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is finite, meaning that the trailing interface is finite in contrast to the case $α$ = 1, but in accordance with $α$ = 0. Finally, the integro-differential system is solved via a fixed-point method.
