Existence of a traveling wave solution in a free interface problem with fractional order kinetics

Journal of Differential Equations(2021)

引用 2|浏览2
暂无评分
摘要
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-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincaré-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.
更多
查看译文
关键词
primary,secondary
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要