Stuart, A. M. (1989) Singular Free Boundary Problems and Local Bifurcation Theory. SIAM Journal on Applied Mathematics, 49 (1). pp. 72-85. ISSN 0036-1399. doi:10.1137/0149004. https://resolver.caltech.edu/CaltechAUTHORS:20170613-080915333
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Abstract
A constructive method applicable to the solution of a wide class of free boundary problems is presented. A solution-dependent transformation technique is introduced. By considering a singular limit of the transformation, a related problem, to which local bifurcation theory may be applied, is derived. By inverting the (near singular) mapping between the two problems, an expression for solutions of the original problem is obtained. The method is illustrated by the study of a singularly perturbed elliptic equation. Approximate solutions are constructed and the validity of the approximations established by means of the Contraction Mapping Theorem.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1989 Society for Industrial and Applied Mathematics. Submitted: 03 August 1987. Accepted: 26 February 1988. | |||||||||
| Subject Keywords: | free boundary problems, bifurcation theory, singular limits | |||||||||
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| Issue or Number: | 1 | |||||||||
| Classification Code: | AMS(MOS) subject classifications. 34A08, 34B15, 35B32, 35R35 | |||||||||
| DOI: | 10.1137/0149004 | |||||||||
| Record Number: | CaltechAUTHORS:20170613-080915333 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170613-080915333 | |||||||||
| Official Citation: | Singular Free Boundary Problems and Local Bifurcation Theory A. M. Stuart SIAM Journal on Applied Mathematics 1989 49:1, 72-85 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 78142 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 13 Jun 2017 16:15 | |||||||||
| Last Modified: | 15 Nov 2021 17:37 |
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