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. doi:10.1093/imamat/38.1.23. 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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| 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. | |||||||||
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| Issue or Number: | 1 | |||||||||
| DOI: | 10.1093/imamat/38.1.23 | |||||||||
| 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: | 15 Nov 2021 17:36 |
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