The solution of one class of dual integral equations connected with the Mehler-Fock transform in the theory of elasticity and mathematical physics

1969 ◽  
Vol 33 (6) ◽  
pp. 1029-1036
Author(s):  
N.N. Lebedev ◽  
I.P. Skal'skaia
Keyword(s):  
Integral Equations ◽  
Mathematical Physics ◽  
Theory Of Elasticity ◽  
Dual Integral Equations

Ian Naismith Sneddon, O.B.E. 8 December 1919 – 4 November 2000

2002 ◽  
Vol 48 ◽  
pp. 417-437 ◽  
Author(s):  
P. Chadwick
Keyword(s):  
World War Ii ◽  
Integral Equations ◽  
Linear Theory ◽  
Analytical Techniques ◽  
Integral Transforms ◽  
Theory Of Elasticity ◽  
World War ◽  
Dual Integral Equations ◽  
Cultural Life ◽  
The University

Ian Sneddon was introduced to problems in the linear theory of elasticity involving the indentation of a surface and the extension of a crack through his work for the Ministry of Supply during World War II. He maintained a lifelong research interest in this area and also made distinguished contributions to a range of related analytical techniques, notably the application of integral transforms and the solution of dual integral equations. His many books, extensive travels and engaging personality made him very well known internationally, and he developed particularly fruitful contacts in the USAand Poland. He gave devoted service to the University of Glasgow, where the bulk of his career was spent, and played an active part in the cultural life of Scotland.

scholarly journals The elementary solution of dual integral equations

1960 ◽  
Vol 4 (3) ◽  
pp. 108-110 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Integral Equations ◽  
Present Note ◽  
Mixed Boundary ◽  
Formal Solution ◽  
Mathematical Physics ◽  
Elementary Solution ◽  
Dual Integral Equations ◽  
Mellin Transforms ◽  
Method Of Solution ◽  
Image Position

When the theory of Hankel transforms is applied to the solution of certain mixed boundary value problems in mathematical physics, the problems are reduced to the solution of dual integral equations of the typewhere α and ν are prescribed constants and f(ρ) is a prescribed function of ρ [1]. The formal solution of these equations was first derived by Titchmarsh [2]. The method employed by Titchmarsh in deriving the solution in the general case is difficult, involving the theory of Mellin transforms and what is essentially a Wiener-Hopf procedure. In lecturing to students on this subject one often feels the need for an elementary solution of these equations, especially in the cases α = ± 1, ν = 0. That such an elementary solution exists is suggested by Copson's solution [3] of the problem of the electrified disc which corresponds to the case α = –l, ν = 0. A systematic use of a procedure similar to Copson's has in fact been made by Noble [4] to find the solution of a pair of general dual integral equations, but again the analysis is involved and long. The object of the present note is to give a simple solution of the pairs of equations which arise most frequently in physical applications. The method of solution was suggested by a procedure used by Lebedev and Uflyand [5] in the solution of a much more general problem.

scholarly journals DUAL INTEGRAL EQUATIONS TECHNIQUE IN ELECTROMAGNETIC WAVE SCATTERING BY A THIN DISK

2009 ◽  
Vol 16 ◽  
pp. 107-126 ◽  
Author(s):  
Mikhail V. Balaban ◽  
Ronan Sauleau ◽  
Trevor Mark Benson ◽  
Alexander I. Nosich
Keyword(s):  
Electromagnetic Wave ◽  
Integral Equations ◽  
Wave Scattering ◽  
Thin Disk ◽  
Dual Integral Equations ◽  
Electromagnetic Wave Scattering
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