التفاصيل البيبلوغرافية
| العنوان: |
Existence of a traveling wave solution in a free interface problem with fractional order kinetics |
| المؤلفون: |
Brauner, Claude-Michel, Roussarie, Robert, Shang, Peipei, Zhang, Linwan |
| سنة النشر: |
2020 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Analysis of PDEs |
| الوصف: |
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 < $\alpha$ < 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{\'e}-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 $\alpha$ = 1, but in accordance with $\alpha$ = 0. Finally, the integro-differential system is solved via a fixed-point method. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2010.15685 |
| رقم الانضمام: |
edsarx.2010.15685 |
| قاعدة البيانات: |
arXiv |