(Bounded) Traveling Combustion Fronts With Degenerate Kinetics

TL;DR

This paper studies the propagation of flame fronts in periodic solids with degenerate kinetic rates, proving the existence of bounded traveling wave solutions even under highly degenerate conditions.

Contribution

It extends previous work by establishing the existence of traveling wave solutions for more general degenerate kinetics, including Arrhenius types.

Findings

Existence of bounded, global traveling wave solutions.

Applicability to physically relevant Arrhenius kinetics.

Extension to more degenerate kinetic models.

Abstract

We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence of travelling wave solutions which are bounded and global. Previous results by the same authors (cf. Alibaud, Namah, On the propagation of a periodic flame front by an Arrhenius kinetic,{\it Interfaces Free Bound.,} 2017) were obtained for essentially positively lower bounded kinetics or eventually which have some very weak degeneracy. Here we consider general degenerate kinetics, including in particular those of Arrhenius type which are commonly used in physics.