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The Quarterly Journal of Mechanics and Applied Mathematics 1983 36(2):237-245; doi:10.1093/qjmam/36.2.237
© 1983 by Oxford University Press
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FURTHER SOLUTIONS OF A FREDHOLM INTEGRAL EQUATION OF THE FIRST KIND ARISING IN ELASTIC HALF-SPACE AND FORCED-CONVECTION PROBLEMS

J. A. BELWARD

( Department of Mathematics, University of Queensland St Lucia, Queensland 4067, Australia )

Solutions of a Fredholm integral equation of the first kind with a difference kernel |x|vKv(x|) (Kv a modified Bessel function), hitherto given for |v|<<<12, are constructed for vgreater double equals12. The equation, which arises in forced-convection and elastic half-space problems, is closely related to an axially symmetric boundary-value problem. Changes to this relationship when vgreater double equals12are explained. Existence and uniqueness properties of the solutions are discussed and some closed-form solutions given in certain special cases.


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