Slow-fast system in Rosales-Majda combustion model with fractional order kinetics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912917510684672 |
|---|---|
| author | Brauner, Claude-Michel Jing, Jinlong Roussarie, Robert |
| author_facet | Brauner, Claude-Michel Jing, Jinlong Roussarie, Robert |
| contents | We consider traveling wave solutions of a one-dimensional model for detonation waves derived by Rosales and Majda, when the reaction order $α$ 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 $β$. Our goal in this paper is to study the bifurcation diagram in the $(β,c)$ 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 Poincaré-Bendixson theorem and the Fenichel theory. Theoretical results are confirmed by numerical computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Slow-fast system in Rosales-Majda combustion model with fractional order kinetics Brauner, Claude-Michel Jing, Jinlong Roussarie, Robert Analysis of PDEs Dynamical Systems 35C07, 34E13, 34C05, 34A26, 80A25 We consider traveling wave solutions of a one-dimensional model for detonation waves derived by Rosales and Majda, when the reaction order $α$ 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 $β$. Our goal in this paper is to study the bifurcation diagram in the $(β,c)$ 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 Poincaré-Bendixson theorem and the Fenichel theory. Theoretical results are confirmed by numerical computations. |
| title | Slow-fast system in Rosales-Majda combustion model with fractional order kinetics |
| topic | Analysis of PDEs Dynamical Systems 35C07, 34E13, 34C05, 34A26, 80A25 |
| url | https://arxiv.org/abs/2602.18841 |