# Slow-fast system in Rosales-Majda combustion model with fractional order kinetics

Source: [Slow-fast system in Rosales-Majda combustion model with fractional order kinetics](<https://www.sota2.com/research/paper/699d30656017c4460ffab248>)

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

Data updated: 2026-02-25T05:00:03.907Z

Authors: Claude-Michel Brauner, Jinlong Jing, Robert Roussarie

Published: 2026-02-21T14:06:40.000Z

## Abstract

We consider traveling wave solutions of a one-dimensional model for detonation waves derived by Rosales and Majda, when the reaction order $\\alpha$ belongs to $\[0,1)$. The chemical kinetics is a simplified Arrhenius law or a Heaviside function. The model in the reaction zone is a slow-fast dynamical system for a vector representing temperature and mass fraction, which depends on the velocity $c$ and small viscosity $\\beta$. Our goal in this paper is to study the bifurcation diagram in the $(\\beta,c)$ parameter space and identify the nature of the trajectories corresponding to viscous shock waves. The demonstrations are based on a variety of techniques including the Poincar\\'e-Bendixson theorem and the Fenichel theory. Theoretical results are confirmed by numerical computations.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2602.18841>)

[PDF](<https://arxiv.org/pdf/2602.18841.pdf>)