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Parabolic Free Boundary Problems Arising in Porous Medium Combustion

Norbury, J. and Stuart, A. M. (1987) Parabolic Free Boundary Problems Arising in Porous Medium Combustion. IMA Journal of Applied Mathematics, 39 (3). pp. 241-257. ISSN 0272-4960. https://resolver.caltech.edu/CaltechAUTHORS:20170613-084535886

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Abstract

A parabolic partial differential equation approximating the evolution of temperature in highly exothermic porous-medium combustion at low driving velocities is examined. The equation is of reaction-diffusion type with a reaction term which is discontinuous as a function of the dependent variable. Firstly the variation of the steady solution set with the scaled heat of the reaction is described and the related time-dependent behaviour analysed. The stability results follow from characterizing the ends of the solution branch and fold points explicitly and deducing global stability results about the whole of the continuous solution branch. The results are used to indicate the parameter regimes and temporal scales on which the small driving velocity approximation ceases to be valid. Secondly the behaviour of the discontinuous partial differential equation is compared with that of a continuous equation which it approximates. This provides justification for the approximation of reaction terms possessing steep gradients by discontinuous functions; the large activation energy limit in porous-medium combustion involves such a process.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1093/imamat/39.3.241DOIArticle
https://academic.oup.com/imamat/article-abstract/39/3/241/825663/Parabolic-Free-Boundary-Problems-Arising-in-Porous?redirectedFrom=fulltextPublisherArticle
Additional Information:© 1987 Oxford University Press. Received: 01 May 1987; Published: 01 September 1987. The second author is grateful to the Science and Engineering Research Council for financial support.
Funders:
Funding AgencyGrant Number
Science and Engineering Research Council (SERC)UNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ6
Issue or Number:3
Record Number:CaltechAUTHORS:20170613-084535886
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170613-084535886
Official Citation:J. NORBURY, A. M. STUART; Parabolic Free Boundary Problems Arising in Porous Medium Combustion. IMA J Appl Math 1987; 39 (3): 241-257. doi: 10.1093/imamat/39.3.241
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78152
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Jun 2017 16:08
Last Modified:03 Oct 2019 18:05

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