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The reduction of a pair of singular integral equations

Published online by Cambridge University Press:  24 October 2008

D. Porter
D. Porter
Affiliation:
Department of Mathematics, University of Reading
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Abstract

A method is derived for converting a pair of coupled singular integral equations of a certain form into a single equation of the same (Cauchy-separable) type. Reduction methods for systems of singular integral equations are generally directed towards the construction of equivalent Fredholm equations. Preservation of the singular nature of the kernel in the reduction process permits the powerful techniques associated with Cauchy kernels to be used in seeking closed solutions of the original pair.

The example given, derived previously from a problem in wave diffraction theory, illustrates many aspects of the method.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 1 , July 1986 , pp. 175 - 182
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Gakhov, F. D.. Boundary Value Problems (Pergamon, 1966).Google Scholar
[2]Muskhelishvili, N. I.. Singular Integral Equations (Noordhoff, 1953).Google Scholar
[3]Peters, A. S.. Pairs of Cauchy singular integral equations and the kernel [b(z) + a(ζ)]/(z-ζ). Commun. Pure Appl. Math. 25 (1972), 369–402.Google Scholar
[4]Peters, A. S.. The solution of a certain non-linear Riemann-Hilbert problem with an application. Commun. Pure Appl. Math. 26 (1973), 87–104.Google Scholar
[5]Porter, D.. On some integral equations with a Hankel function kernel. IMA J. Appl. Math. 33 (1984), 211–228.CrossRefGoogle Scholar
[6]Porter, D.. On some Cauchy-separable integral equations. Math. Proc. Cambridge Philos. Soc. 99 (1986), 547–564.Google Scholar
[7]Vekua, N. P.. Systems of Singular Integral Equations (Noordhoff, 1967).Google Scholar