Norbury, J. and Stuart, A. M. (1988) Travelling Combustion Waves in a Porous Medium. Part I—Existence. SIAM Journal on Applied Mathematics, 48 (1). pp. 155-169. ISSN 0036-1399. doi:10.1137/0148007. https://resolver.caltech.edu/CaltechAUTHORS:20170612-165322289
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Abstract
A one-space-dimensional, time-dependent model for travelling combustion waves in a porous medium is analysed. The key variables are the temperature of the solid medium and its density and the temperature of the gaseous phase and its density. The key parameters µ, λ and a are related (respectively) to the driving gas velocity, the specific heat of the combustible solid and the ratio of consumption of oxygen to that of solid. The regions of existence of the different types of combustion waves are found in µ, λ parameter space, with a = 0. The types of combustion wave are classified by the switch mechanism that turns off the combustion, which occurs over a finite, but unknown, interval. Because the model is linear outside the combustion zone, the eigenvalue problem governing the existence of travelling waves may be reformulated as a two-point free boundary problem on a finite domain. Existence and nonexistence theorems are established for this unusual bifurcation problem.
Item Type: | Article | |||||||||
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Additional Information: | © 1988 Society for Industrial and Applied Mathematics. Received by the editors August 11, 1986; accepted for publication (in revised form) April 23, 1987. The work of this author was supported by the Science and Engineering Research Council of the United Kingdom. | |||||||||
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Subject Keywords: | combustion, travelling waves, existence | |||||||||
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Issue or Number: | 1 | |||||||||
Classification Code: | AMS(MOS) subject classifications. 34B15, 35B32, 80A30 | |||||||||
DOI: | 10.1137/0148007 | |||||||||
Record Number: | CaltechAUTHORS:20170612-165322289 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170612-165322289 | |||||||||
Official Citation: | Travelling Combustion Waves in a Porous Medium. Part I—Existence J. Norbury and A. M. Stuart SIAM Journal on Applied Mathematics 1988 48:1, 155-169 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 78135 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | George Porter | |||||||||
Deposited On: | 13 Jun 2017 14:47 | |||||||||
Last Modified: | 15 Nov 2021 17:37 |
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