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August  2009, 24(3): 809-826. doi: 10.3934/dcds.2009.24.809

On the stability of high Lewis number combustion fronts

Anna Ghazaryan 1, and  Christopher K. R. T. Jones 1,

1. 

Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States, United States

Received  February 2008 Revised  June 2008 Published  April 2009

We consider wavefronts that arise in a mathematical model for high Lewis number combustion processes. An efficient method for the proof of the existence and uniqueness of combustion fronts is provided by geometric singular perturbation theory. The fronts supported by the model with very large Lewis numbers are small perturbations of the front supported by the model with infinite Lewis number. The question of stability for the fronts is more complicated. Besides discrete spectrum, the system possesses essential spectrum up to the imaginary axis. We show how a geometric approach which involves construction of the Stability Index Bundles can be used to relate the spectral stability of wavefronts with high Lewis numbers to the spectral stability of the front in the case of infinite Lewis number. We discuss the implication for nonlinear stability of fronts with high Lewis numbers. This work builds on the ideas developed by Gardner and Jones [12] and generalized in the papers by Bates, Fife, Gardner and Jones [3, 4].
Keywords: Traveling wave, high Lewis number, slow - fast dynamics, combustion front., stability index.
Mathematics Subject Classification: Primary: 35B35, 80A25; Secondary: 35K57, 34C3.
Citation: Anna Ghazaryan, Christopher K. R. T. Jones. On the stability of high Lewis number combustion fronts. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 809-826. doi: 10.3934/dcds.2009.24.809
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