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Potential problems involving an annulus

Published online by Cambridge University Press:  24 October 2008

D. L. Clements
Affiliation:
Department of Applied Mathematics, University of Western Ontario, Canada
E. R. Love
Affiliation:
Department of Mathematics, University of Melbourne, Australia

Extract

In electrostatic, elastostatic and hydrodynamic problems involving a plane annulus in space, two mixed boundary value potential problems are frequently encountered. For reasons given below, we consider here the axisymmetric cases of them; and we describe them using cylindrical polar coordinates (r, θ, z) so chosen that the annulus is a < r < b, z = 0.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Copson, E. T.On the problem of the electrified disc. Proc. Edinburgh Math. Soc. (II) 8 (1947), 1419. MR 9 no. 318.CrossRefGoogle Scholar
(2)Gubenko, V. S. and Mossakovskii, V. I.Pressure of an axially symmetric circular die on an elastic half space. Prikl. Mat. Meh. 24 (1960), 334340 (Russian); translated in J. Appl. Math. Mech. 24 (1960), 477–486. MR 22 no. 8804.Google Scholar
(3)Collins, W. D.On the solution of some axisymmetric boundary value problems by means of integral equations. VIII. Potential problems for a circular annulus. Proc. Edinburgh Math. Soc. (II) 13 (1963), 235246. MR 28 no. 439.CrossRefGoogle Scholar
(4)Noble, B.The solution of Bessel function dual integral equations by a multiplying-factor method. Proc. Cambridge Philos. Soc. 59 (1963), 351362. MR 26 no. 2842.CrossRefGoogle Scholar
(5)Cooke, J. C.Some further triple integral equation solutions. Proc. Edinburgh Math. Soc. (II) 13 (1963), 303316. MR 28 no. 4313.CrossRefGoogle Scholar
(6)Williams, W. E.Integral equation formulation of some three-part boundary value problems. Proc. Edinburgh Math. Soc. (II) 13 (1963), 317323. MR 28 no. 4314.CrossRefGoogle Scholar