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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

On the stability of high Lewis number combustion fronts

Pages: 809 - 826, Volume 24, Issue 3, July 2009

doi:10.3934/dcds.2009.24.809       Abstract        Full Text (245.0K)       Related Articles

Anna Ghazaryan - Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States (email)
Christopher K. R. T Jones - Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States (email)

Abstract: 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, stability index, slow - fast dynamics, high Lewis number, combustion front.
Mathematics Subject Classification:  Primary: 35B35, 80A25; Secondary: 35K57, 34C37.

Received: February 2008;      Revised: June 2008;      Published: April 2009.