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On the direct solution of certain half-plane mixed boundary-value problems

Published online by Cambridge University Press:  24 October 2008

D. Naylor
D. Naylor
Affiliation:
University of WesternOntario
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In this paper a method is proposed for solving certain half-plane elliptic boundary-value problems involving mixed boundary conditions. The equation considered is a generalization of the Tricomi equation which contains the space form of the damped wave equation as a special case. Existing methods depend on the use of Fourier integrals and lead to the solution of integral equations. The methods employed here are direct and yield explicit solution formulas without the necessity of solving integral equations and as such avoid the arguments inherent in the use of the Wiener-Hopf technique.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 753 - 759
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Carrier, G. F.A generalisation of the Wiener-Hopf technique. Quart. Appl. Math. 7 (1949), 105–109.CrossRefGoogle Scholar
(2)Chang, C. C. and Lundgren, T. S.Airfoil in a sonic shear flow jet: A mixed boundary value problem for the generalised Tricomi equation. Quart. Appl. Math. 17 (1960), 375–392.CrossRefGoogle Scholar
(3)Eedelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, volume 1 (McGraw-Hill, 1953).Google Scholar
(4)Evvard, J. C.Use of source distributions for evaluating theoretical aerodynamics of thin finite wings at supersonic speeds. N.A.C.A. Report no. 951 (1949).Google Scholar
(5)Gunn, J. C.Linearised supersonic aerofoil theory. Philos. Trans. Roy. Soc. London, Ser. A 240 (1947), 327–373.Google Scholar
(6)Hobson, E. W.The theory of spherical and ellipsoidal harmonics (Cambridge University Press, 1931).Google Scholar
(7)Miles, J. W.The oscillating rectangular airflow at supersonic speeds. Quart. Appl. Math. 9 (1951), 47–65.Google Scholar
(8)Miles, J. W.The potential theory of unsteady supersonic flow (Cambridge University Press, 1959).Google Scholar
(9)Naylor, D.On a Mellin type integral transform. J. Math. Mech. 12 (1963), 265–274.Google Scholar
(10)Naylor, D.On a finite Lebedev transform. J. Math. Mech. 12 (1963), 375–384.Google Scholar
(11)Naylor, D.An eigenvalue problem in cylindrical harmonics. J. Math. Phys. 44 (1965), 391–402.Google Scholar
(12)Naylor, D.On a Sturm–Liouville expansion in series of Bessel functions. Proc. Cambridge Philos. Soc. 62 (1966), 61–72.Google Scholar
(13)Naylor, D.On a finite Lebedev transform, Part 2. J. Math. Mech. 15 (1966), 455–464.Google Scholar
(14)Watson, G. N.Theory of Bessel functions, second edition (Cambridge University Press, 1958).Google Scholar
(15)Williams, W. E.A class of mixed boundary value problems. J. Math. Mech. 11 (1962), 109–119.Google Scholar