Geodesic
The solution of certain simultaneous pairs of dual integral equations†
Glasgow mathematical journal, Tome 9 (1968) no. 2, pp. 92-102

Voir la notice de l'article provenant de la source Cambridge University Press

In the analysis of mixed boundary value problems by Hankel transforms, one often encounters dual integral equations of the formwhere I1 = (0, 1), I2 = (1, ∞); w1(x), w2(x) are weight functions, ψ(x) is the unknown function, and f(y), g(y) are functions continuously differentiate on I1 and I2 respectively. Many successful attempts have been made to solve (1.1) and (1.2). These are all discussed in a recent book by Sneddon [7]. As pointed out in a recent paper by Erdogan and Bahar [4], in mixed boundary value problems of semi-infinite domains involving more than one unknown function such as those arising in elastostatics, viscoelasticity, and electrostatics, the formulation will lead to a system of simultaneous dual integral equations which is a generalization of (1.1) and (1.2). These equations may be expressed as follows:with i = 1, 2, ..., n, where we use the notation 
Lowengrub, M. The solution of certain simultaneous pairs of dual integral equations†. Glasgow mathematical journal, Tome 9 (1968) no. 2, pp. 92-102. doi: 10.1017/S0017089500000355
@article{10_1017_S0017089500000355,
     author = {Lowengrub, M.},
     title = {The solution of certain simultaneous pairs of dual integral equations{\textdagger}},
     journal = {Glasgow mathematical journal},
     pages = {92--102},
     year = {1968},
     volume = {9},
     number = {2},
     doi = {10.1017/S0017089500000355},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000355/}
}
TY  - JOUR
AU  - Lowengrub, M.
TI  - The solution of certain simultaneous pairs of dual integral equations†
JO  - Glasgow mathematical journal
PY  - 1968
SP  - 92
EP  - 102
VL  - 9
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000355/
DO  - 10.1017/S0017089500000355
ID  - 10_1017_S0017089500000355
ER  - 
%0 Journal Article
%A Lowengrub, M.
%T The solution of certain simultaneous pairs of dual integral equations†
%J Glasgow mathematical journal
%D 1968
%P 92-102
%V 9
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000355/
%R 10.1017/S0017089500000355
%F 10_1017_S0017089500000355

[1] 1.Abramowitz, M. and Stetgun, I. A., Handbook of mathematical functions (Nat. Bureau of Standards, App. Math. Series 55, 1964). Google Scholar

[2] 2.Copson, E. T., On certain dual integral equations, Proc. Glasgow Math. Assoc. 5 (1961), 21–24. Google Scholar | DOI

[3] 3.Erdelyi, A. and Sneddon, I. N., Fractional integration and dual integral equations, Canad. J. Math. 14 (1962), 685–693. Google Scholar | DOI

[4] 4.Erdogan, F. and Bahar, L. Y., On the solution of simultaneous dual integral equations, S.I.A.M. Journal 12 (1964), 666–675. Google Scholar

[5] 5.Lowengrub, M. and Sneddon, I. N., The solution of a pair of dual integral equations, Proc. Glasgow Math. Assoc. 6 (1963), 14–18. Google Scholar | DOI

[6] 6.Peters, A. S., Certain dual integral equations and Sonine's integral (Technical report Imm-NYU 285, Inst. Math. Sci. NYU 08, 1961). Google Scholar

[7] 7.Sneddon, I. N., Mixed boundary value problems of potential theory (North Holland Publishing Co. Amsterdam, 1966). Google Scholar

[8] 8.Sneddon, I. N. and Lowengrub, M., Crack problems in the classical theory of elasticity (New York, 1968). Google Scholar

[9] 9.Tranter, C. J., Integral Transforms in Mathematical Physics (New York, 1956). Google Scholar

[10] 10.Westmann, R. A., Simultaneous pairs of dual integral equations, SIAM Rev. 7 (1965), 341–348. Google Scholar | DOI

Cité par Sources :