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Some Further Triple Integral Equation Solutions

Published online by Cambridge University Press:  20 January 2009

J. C. Cooke
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A solution of a triad of integral equations involving Bessel functions is given. This, like earlier ones, is in the form of a pair of Fredholm integral equations, which may be solved by iteration in certain cases. In spite of a slightly more general formulation of the problem, the kernels of these equations are simpler than those given in earlier solutions. Certain extensions are considered and a formal solution given. Application is made to the problem of incompressible inviscid flow normal to an annular disc, and to the flow due to the slow rotation of such a disc in a viscous fluid.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 4 , December 1963 , pp. 303 - 316
Copyright
Copyright © Edinburgh Mathematical Society 1963

References

REFERENCES

Helliwell, J. B.J. Math. Phys., 40 (1961), 1.CrossRefGoogle Scholar
Tranter, C. J.Proc. Glas. Math. Assoc., 4 (1960), 401.Google Scholar
Gubenko, V. S. and Mossakovskii, V. I., P.M.M., 24 (1960), 200.Google Scholar
Smythe, W. R.Amer. J. App. Phys., 22 (1951), 1499.CrossRefGoogle Scholar
Collins, W. D.Arch. Rat. Mech. Anal., 11 (1962), 122.CrossRefGoogle Scholar
Cooke, J. C.Quart. J. Mech. App. Math., 16 (1963), 193.CrossRefGoogle Scholar
Williams, W. E.Quart. J. Mech. App. Math., 16 (1963), 204.CrossRefGoogle Scholar
Noble, B.Proc. Camb. Phil. Soc., 59 (1963), 351.CrossRefGoogle Scholar
Williams, W. E. to be published.Google Scholar
Noble, B.J. Math. Phys., 37 (1958), 128.CrossRefGoogle Scholar
Lamb, H.Hydrodynamics (Cambridge, 1932).Google Scholar
Jeffery, G. B.Proc. Lond. Math. Soc. (2), 14 (1915), 327.CrossRefGoogle Scholar
Erdelyi, A. (ed.), Higher Transcendental Functions, Vol. 1 (New York, 1953)Google Scholar