# Uniqueness of traveling fronts in premixed flames with stepwise ignition-temperature kinetics and fractional reaction order

Source: [Uniqueness of traveling fronts in premixed flames with stepwise ignition-temperature kinetics and fractional reaction order](<https://www.sota2.com/research/paper/68fa46721e209131ce92084a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T05:49:58.848Z

Authors: Amanda Matson, Claude-Michel Brauner, Peter V. Gordon

Published: 2023-05-05T16:20:12.000Z

## Abstract

In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in \[3\] that this system admits a traveling front solution. In the present work, we show that this traveling front is unique up to translations. We also study some qualitative properties of this solution using the combination of formal asymptotics and numerics. Our findings allow conjecture that the velocity of the propagation of the flame front is a decreasing function of all of the parameters of the problem: ignition temperature, reaction order and an inverse of the Lewis number.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2305.03654>)

[PDF](<https://arxiv.org/pdf/2305.03654.pdf>)