Traveling wave solutions of a 3-component reaction-diffusionmodel in smoldering combustion

Kota Ikeda; Masayasu Mimura

doi:10.3934/cpaa.2012.11.275

Article Contents

2012, Volume 11, Issue 1: 275-305. Doi: 10.3934/cpaa.2012.11.275

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Traveling wave solutions of a 3-component reaction-diffusion model in smoldering combustion

Kota Ikeda^1, and
Masayasu Mimura^2,

1.
Graduate School of Advanced Mathematical Science, Meiji University, Kawasaki, 214-8571
2.
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Kawasaki, 214-8571

Received: July 31, 2010

Revised: December 31, 2010

Published: December 2011

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Abstract

We are concerned with a reaction diffusion model describing slow smoldering combustion. The process consists of a sheet of paper ignited on one side and in the presence of a flow of air confined in a narrow gap above the paper. It is observed that thermal-diffusion instability generates diverse spatial patterns in combustion front propagation, depending on flow velocity of gas supply. Particularly, if the velocity is rather fast, planar front propagating with almost constant velocity appears. Motivated by this observation, we discuss the existence and stability of $1$ dimensional traveling wave solutions of the model.

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Mathematics Subject Classification: Primary: 35B25, 35B35; Secondary: 35K57, 35P15.

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