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Closed form solution to some mixed boundary value problems for a charged sphere

Published online by Cambridge University Press:  17 February 2009

V. I. Fabrikant
V. I. Fabrikant
Affiliation:
Department of Mechanical Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada.
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Abstract

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A new method is described which allows an exact solution in a closed form to the following non-axisymmetric mixed boundary-value problem for a charged sphere: arbitrary potential values are given at the surface of a spherical segment while an arbitrary charge distribution is prescribed on the rest of the sphere. The method is founded on a new integral representation of the kernel of the governing integral equation. Several examples are considered. All the results are expressed in elementary functions. Some further applications of the method are discussed. No similar result seems to have been published previously.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 3 , January 1987 , pp. 296 - 309
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Collins, W. D., “On the solution of some axisymmetric boundary value problems by means of integral equations”, Quart. J. Mech. Appl. Math. 12 pt. 2, (1959), 232–241.CrossRefGoogle Scholar
[2]Fabrikant, V. I. and Sankar, T. S., “On contact problems in inhomogeneous half-space”, Internat. J. Solids and Structures 20 (1984), 159–166.CrossRefGoogle Scholar
[3]Hobson, E. W., “On Green's function for a circular disc, with application to electrostatic problems”, Trans. Cambridge Phil. Soc. 18 (1900), 277–291.Google Scholar
[4]Lur'e, A. I., Three-dimensional problems of the theory of elasticity (Interscience Publishers, New York, 1964).Google Scholar
[5]Sneddon, I. N., Mixed boundary value problems in potential theory (North-Holland Publishing Company, Amsterdam, 1966).Google Scholar
[6]Uflyand, Ya. S., Method of dual equations in mathematical physics (Nauka, Leningrad, 1977) (in Russian).Google Scholar