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Travelling Combustion Waves in a Porous Medium. Part I—Existence

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.

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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.
Funding AgencyGrant Number
Science and Engineering Research Council (SERC)UNSPECIFIED
Subject Keywords:combustion, travelling waves, existence
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ4
Issue or Number:1
Classification Code:AMS(MOS) subject classifications. 34B15, 35B32, 80A30
Record Number:CaltechAUTHORS:20170612-165322289
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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
Deposited By: George Porter
Deposited On:13 Jun 2017 14:47
Last Modified:15 Nov 2021 17:37

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