SLOW-FAST SYSTEM IN ROSALES-MAJDA COMBUSTION MODEL WITH FRACTIONAL ORDER KINETICS
Résumé
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.
Mots clés
- 2020 Mathematics Subject Classification. 35C07 34E13 34C05 34A26 80A25 Traveling reactive shock waves slow-fast differential systems Poincaré-Bendixson theory bifurcation diagram free interface combustion
- 2020 Mathematics Subject Classification. 35C07
- 34E13
- 34C05
- 34A26
- 80A25 Traveling reactive shock waves
- slow-fast differential systems
- Poincaré-Bendixson theory
- bifurcation diagram
- free interface
- combustion
Domaines
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