Communications on Pure and Applied Analysis (CPAA)

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

Pages: 275 - 305, Volume 11, Issue 1, January 2012      doi:10.3934/cpaa.2012.11.275

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Kota Ikeda - Graduate School of Advanced Mathematical Science, Meiji University, Kawasaki, 214-8571, Japan (email)
Masayasu Mimura - Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Kawasaki, 214-8571, Japan (email)

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.

Keywords:  Combustion model, traveling wave solution, fingering pattern, stability.
Mathematics Subject Classification:  Primary: 35B25, 35B35; Secondary: 35K57, 35P15.

Received: August 2010;      Revised: January 2011;      Available Online: September 2011.