Stability of interacting traveling waves in reaction-convection-diffusion systems. (English) Zbl 1333.76074
Summary: The stability of isolated combustion traveling waves has been exhaustively studied in the literature of reaction-diffusion systems. The analysis has been done mainly by neglecting other waves that are usually present in the solution and that can influence the stability of the combustion wave. In this paper, a numerical example on the influence of such interaction on wave stability are presented.
The paper is illustrated through a simple model for the injection of air into a porous medium that contains a solid fuel. The model considered here reproduces a variety of observed phenomena and yet is simple enough to allow rigorous investigation. We refer on earlier work containing proofs of existence of traveling waves corresponding to combustion waves by phase plane analysis were presented; wave sequences that can occur as solutions of Riemann problems were identified.
The paper is illustrated through a simple model for the injection of air into a porous medium that contains a solid fuel. The model considered here reproduces a variety of observed phenomena and yet is simple enough to allow rigorous investigation. We refer on earlier work containing proofs of existence of traveling waves corresponding to combustion waves by phase plane analysis were presented; wave sequences that can occur as solutions of Riemann problems were identified.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 35C07 | Traveling wave solutions |
| 35B35 | Stability in context of PDEs |
| 80A25 | Combustion |
Keywords:
traveling wave; Riemann problem; filtration combustion; stability; combustion in porous media; ignition; extinctionReferences:
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