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Nonlinear Sciences > Pattern Formation and Solitons

arXiv:nlin/0612023 (nlin)
[Submitted on 11 Dec 2006]

Title:High Lewis number combustion wavefronts: a perturbative Melnikov analysis

Authors:S. Balasuriya, G.A. Gottwald, J. Hornibrook, S. Lafortune
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Abstract: The wavefronts associated with a one-dimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situation, in which fuel diffusivity is small in comparison to that of heat, is appropriate for highly dense fluids. A formula for the wavespeed is established by a non-standard application of Melnikov's method and slow manifold theory from dynamical systems, and compared to numerical results. A simple characterization of the wavespeed correction is obtained: it is proportional to the ratio between the exothermicity parameter and the Lewis number. The perturbation method developed herein is also applicable to more general coupled reaction-diffusion equations with strongly differing diffusivities. The stability of the wavefronts is also tested using a numerical Evans function method.
Comments: accepted for publication by SIAM Journal on Applied Mathematics
Subjects: Pattern Formation and Solitons (nlin.PS)
Cite as: arXiv:nlin/0612023 [nlin.PS]
  (or arXiv:nlin/0612023v1 [nlin.PS] for this version)
  https://doi.org/10.48550/arXiv.nlin/0612023

Submission history

From: Georg Gottwald A. [view email]
[v1] Mon, 11 Dec 2006 21:47:57 UTC (169 KB)
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