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Existence of Solutions of a Two-Point Free-Boundary Problem Arising in the Theory of Porous Medium Combustion

Stuart, A. M. (1987) Existence of Solutions of a Two-Point Free-Boundary Problem Arising in the Theory of Porous Medium Combustion. IMA Journal of Applied Mathematics, 38 (1). pp. 23-34. ISSN 0272-4960. https://resolver.caltech.edu/CaltechAUTHORS:20170612-142648576

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Abstract

The existence of solutions of a two-point free-boundary problem arising from the theory of travelling combustion waves in a porous medium is examined. The problem comprises a third-order nonlinear ordinary differential equation posed on an unknown interval of finite length; four boundary conditions are given, two at either end of the interval. The equations possess a trivial solution for all values of the bifurcation parameter λ. A shooting technique is employed to prove the existence of a nontrivial solution for 0 < λ< λ_c and nonexistence theorems are proved for λ ∉ (0, λ_c ).


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https://doi.org/10.1093/imamat/38.1.23DOIArticle
https://academic.oup.com/imamat/article-abstract/38/1/23/644891/Existence-of-Solutions-of-a-Two-Point-Free?redirectedFrom=fulltextPublisherArticle
Additional Information:© 1987 Oxford University Press. Received: 27 November 1986. Revision Received: 23 March 1987. Published: 01 January 1987. I am extremely grateful to Dr. John Norbury for valuable discussions on various aspects of this work. I also wish to thank the Science and Engineering Research Council for funding this work.
Funders:
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Science and Engineering Research Council (SERC)UNSPECIFIED
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ3
Issue or Number:1
Record Number:CaltechAUTHORS:20170612-142648576
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170612-142648576
Official Citation:A. M. STUART; Existence of Solutions of a Two-Point Free-Boundary Problem Arising in the Theory of Porous Medium Combustion. IMA J Appl Math 1987; 38 (1): 23-34. doi: 10.1093/imamat/38.1.23
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78123
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2017 21:57
Last Modified:03 Oct 2019 18:05

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