Singular perturbation solution of a class of singular integral equations

Authors:
J. R. Willis and S. Nemat-Nasser

Journal:
Quart. Appl. Math. **48** (1990), 741-753

MSC:
Primary 45E99; Secondary 73M25

DOI:
https://doi.org/10.1090/qam/1079917

MathSciNet review:
MR1079917

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Abstract | References | Similar Articles | Additional Information

Abstract: A formal method is developed for finding asymptotic solutions to a class of strongly singular integral equations containing a small parameter, . The class has relevance to the analysis of microcrack growth in reinforced ceramics. The method makes use of the asymptotic matching principle of Van Dyke. Its application is mechanical and it appears to allow, in principle, the construction of asymptotic solutions to any order. Consistency to order is demonstrated for the general case and a solution correct to order is constructed for a particular example, previously studied only to leading order.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1079917

Article copyright:
© Copyright 1990
American Mathematical Society