Stability of interacting traveling waves in reaction-convection-diffusion systems

Grigori  Chapiro; Lucas  Furtado; Dan  Marchesin; Stephen Schecter

doi:10.3934/proc.2015.0258

Article Contents

2015, Volume 2015: 258-266. Doi: 10.3934/proc.2015.0258 open access

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Stability of interacting traveling waves in reaction-convection-diffusion systems

1.
Universidade Federal de Juiz de Fora, Juiz de Fora, MG 36036-900
2.
Columbia College, Columbia University, New York, NY 10027
3.
Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, RJ 22460-320
4.
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 76S05, 35C07, 35B35; Secondary: 80A25.

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