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On the stability of high Lewis number combustion fronts
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Ghazaryan, Anna and Jones, C. K. R. T. (Christopher K. R. T.) (2009) On the stability of high Lewis number combustion fronts. Discrete and Continuous Dynamical Systems, Vol.24 (No.3 Sp. Iss. SI). pp. 809-826. doi:10.3934/dcds.2009.24.809 ISSN 1078-0947.
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Official URL: http://dx.doi.org/10.3934/dcds.2009.24.809
Abstract
We consider wave fronts 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 possess 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].
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Discrete and Continuous Dynamical Systems | ||||
| Publisher: | American Institute of Mathematical Sciences | ||||
| ISSN: | 1078-0947 | ||||
| Official Date: | July 2009 | ||||
| Dates: |
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| Volume: | Vol.24 | ||||
| Number: | No.3 Sp. Iss. SI | ||||
| Number of Pages: | 18 | ||||
| Page Range: | pp. 809-826 | ||||
| DOI: | 10.3934/dcds.2009.24.809 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | National Science Foundation (U.S.) (NSF) | ||||
| Grant number: | DMS-0410267 |
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