Boundary value problems in diffraction theory and lifting surface theory
Compositio Mathematica, Volume 16 (1964), p. 205-293
@article{CM_1964__16__205_0,
     author = {Boersma, J.},
     title = {Boundary value problems in diffraction theory and lifting surface theory},
     journal = {Compositio Mathematica},
     publisher = {Kraus Reprint},
     volume = {16},
     year = {1964},
     pages = {205-293},
     zbl = {0166.37802},
     mrnumber = {174252},
     language = {en},
     url = {http://www.numdam.org/item/CM_1964__16__205_0}
}
Boersma, J. Boundary value problems in diffraction theory and lifting surface theory. Compositio Mathematica, Volume 16 (1964) pp. 205-293. http://www.numdam.org/item/CM_1964__16__205_0/

H. Bateman [1] The solution of partial differential equations by means of definite integrals. Proc. London Math. Soc. 2, 451-458 (1904). | JFM 35.0363.01

J. Bazer and A. Brown [2] a. Diffraction of scalar waves by a circular aperture. New York Univ., Inst. Math. Sci., Div. Electromagnetic Res., Res. Rep. No. EM-144 (1959).

b. IRE Trans. on Antennas and Propagation AP-7, 12-20 (1959).

J. Bazer and H. Hochstadt [3] a. Diffraction of scalar waves by a circular aperture. II. New York Univ., Inst. Math. Sci., Div. Electromagnetic Res., Res. Rep. No. EM-170 (1961).

b. Comm. Pure Appl. Math. 15, 1-33 (1962). | Zbl 0107.43806

J.P. Benkard [4] On an axisymmetrical vector boundary value problem with special reference to the circular disk. Dissertation, University of Michigan, 1961.

C.J. Bouwkamp [5] On the freely vibrating circular disk and the diffraction by circular disks and apertures. Physica 16, 1-16 (1950). | MR 35607 | Zbl 0040.12001

[6] On the diffraction of electromagnetic waves by small circular disks and holes. Philips Res. Rep. 5, 401-422 (1950).

[7] Diffraction theory, a critique of some recent developments. New York Univ., Inst. Math. Sci., Div. Electromagnetic Res., Res. Rep. No. EM-50 (1958).

[8] Diffraction theory. Rep. Progr. Phys. 17, 35-100 (1954). | Zbl 0059.20809

W.D. Collins [9] On the solution of some axisymmetric boundary value problems by means of integral equations. a. I. Quart. J. Mech. Appl. Math. 12, 232-241 (1959). | Zbl 0085.41304

b. II. Mathematika 6, 120-188 (1959). | MR 116861

c. III. Proc. London Math. Soc. (3), 10, 428-460 (1960).

d. IV. Proc. Edinburgh Math. Soc. (2), 12, 95-106 (1960). | MR 126559 | Zbl 0099.21902

e. V. Quart. J. Mech. Appl. Math. 14, 101-117 (1961).

f. VI. Proc. London Math. Soc., to be published.

g. VII. Proc. Edinburgh Math. Soc. (2), 13, 13-23 (1962). | Zbl 0113.20503

h. VIII. Proc. Edinburgh Math. Soc. (2), 13, 235-246 (1968). | Zbl 0124.30805

E.T. Copson [10] On the problem of the electrified disc. Proc. Edinburgh Math. Soc. (2), 8, 14-19 (1947). | MR 23192

W.H. Eggimann [11] Higher-order evaluation of electromagnetic diffraction by circular disks. IRE Trans. on Microwave Theory and Techniques MTT-9, 408-418 (1961).

A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi [12] Higher transcendental functions, vol. I, II. New York, 1958. | Zbl 0051.30303

[13] Tables of integral transforms, vol. I. New York, 1954.

A.E. Green and W. Zerna [14] Theoretical elasticity. Oxford, 1954. | MR 64598 | Zbl 0056.18205

G.A. Grinbergand Iu.. V. Pimenov [15] On the question of diffraction of electromagnetic waves from infinitesimally thin ideally conducting plane screens. Soviet Physics Tech. Phys. 2, 2160- 2175 (1957).

A.E. Heins [16] Function-theoretic aspects of diffraction theory. Proc. Symposium on Electromagnetic Waves, 99-108. Madison, 1962. | MR 133658

A.E. Heins and R.C. Maccamy [17] On the scattering of waves by a disk. Z. Angew. Math. Phys. 11, 249-264 (1960) | Zbl 0119.21902

P. Henrici [18] Zur Funktionentheorie der Wellengleichung. Comment. Math. Helv. 27, 235-293 (1953). | Zbl 0052.33002

H. Hönl, A.W. Maue and K. Westpfahl [19] Theorie der Beugung. Handbuch der Physik, Bd. XXV/1, 218-592. Berlin, 1961. | MR 177615

A.T. De Hoop [20] On the scalar diffraction by a circular aperture in an infinite plane screen. Appl. Sci. Res. B4, 151-160 (1954). | Zbl 0057.42706

[21] Variational formulation of two-dimensional diffraction problems with application to diffraction by a slit. Nederl. Akad. Wetensch. Proc. Ser. B, 58, 401-411 (1955). | Zbl 0066.43503

R.A. Hurd [22] A note on the diffraction of a scalar wave by a small circular aperture. Canad. J. Phys. 39, 1065-1070 (1961). | Zbl 0119.22902

D.S. Jones [23] A new method for calculating scattering with particular reference to the circular disc. Comm. Pure Appl. Math. 9, 713-746 (1956). | Zbl 0073.43202

D.S. Jones and B. Noble [24] The low-frequency scattering by a perfectly conducting strip. Proc. Cambridge Philos. Soc. 57, 364-366 (1961). | Zbl 0105.20801

W. Kinner [25] Die kreisförmige Tragfläche auf potentialtheoretischer Grundlage. Ing.-Arch. 8, 47-80 (1937). | JFM 63.0774.04

K. Krienes and Th. Schade [26] Theorie der schwingenden kreisförmigen Tragfläche auf potentialtheoretischer Grundlage. II. Numerischer Teil. Luftfahrtforschung 19, 282-299 (1942). | MR 7675 | Zbl 0061.44703

V.N. Kuritsyn [27] Arbitrary incidence of a plane electromagnetic wave on a conducting disk. Soviet Physics Tech. Phys. 5, 744-752 (1961).

N.N. Lebedev and I.P. Skal'Skaya [28] A new method for solving the problem of the diffraction of electromagnetic waves by a thin conducting disk. Soviet Physics Tech. Phys. 4, 627-637 (1959)

H.C. Levey and P.E. Wynter [29] The circular wing and related problems. Proc. Roy. Soc. Ser. A, 268, 390-404 (1962). | Zbl 0111.38001

L.A. Ljusternik and W.I. Sobolew [30] Elemente der Funktionalanalysis. Berlin, 1960.

E.R. Love [31] The electrostatic field of two equal circular co-axial conducting disks. Quart. J. Mech. Appl. Math. 2, 428-451 (1949). | Zbl 0040.12105

K.A. Lur'E [82] Diffraction of a plane electromagnetic wave on an ideally conducting circular disk. Soviet Physics Tech. Phys. 4, 1313-1325 (1960).

W. Magnus [33] Infinite matrices associated with diffraction by an aperture. Quart. Appl. Math. 11, 77-86 (1953). | Zbl 0053.15905

[34] An infinite system of linear equations arising in diffraction theory. New York Univ., Inst. Math. Sci., Div. Electromagnetic Res., Res. Rep. No. EM-80 (1955).

J. Meixner [35] Strenge Theorie der Beugung elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe. Z. Naturforsch. 3a, 506-518 (1948). | MR 31369 | Zbl 0033.08903

[36] Theorie der Beugung elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe und verwandte Probleme. Ann. Physik (6), 12, 227-236 (1953). | Zbl 0051.19703

J. Meixner and W. Andrejewski [37] Strenge Theorie der Beugung ebener elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe und an der kreisförmigen Öffnung im vollkommen leitenden ebenen Schirm. Ann. Physik (6), 7, 157-168 (1950). | Zbl 0036.42001

R.F. Millar [88] A note on diffraction by an infinite slit. Canad. J. Phys. 38, 38-47 (1960). | Zbl 0089.20601

P.M. Morse and P.J. Rubenstein [89] The diffraction of waves by ribbons and by slits. Phys. Rev. 54, 895-898 (1938). | JFM 64.1178.03 | Zbl 0020.17705

R. Müller and K. Westpfahl [40] Eine strenge Behandlung der Beugung elektromagnetischer Wellen am Spalt. Z. Physik 134, 245-263 (1953). | Zbl 0050.20904

B. Noble [41] Integral equation perturbation methods in low-frequency diffraction. Proc. Symposium on Electromagnetic Waves, 323-360. Madison, 1962.

Th. Schade [42] Theorie der schwingenden kreisförmigen Tragfläche auf potentialtheoretischer Grundlage. I. Analytischer Teil. Luftfahrtforschung 17, 387-400 (1940). | JFM 66.1100.01 | Zbl 0063.06760

A. Sommerfeld [48] Optics. Lectures on theoretical physics, vol. IV. New York, 1964. | Zbl 0058.22104

E. Van Spiegel [44] Boundary value problems in lifting surface theory. Dissertation, Technological University Delft, 1959. | MR 108955

F.G. Tricomi [45] Integral equations. New York, 1957. | MR 94665 | Zbl 0078.09404

A.I. Van De Vooren [46] Unsteady airfoil theory. Advances in Applied Mechanics, vol. V, 35-89. New York, 1958. | Zbl 0083.19802

G.N. Watson [47] A treatise on the theory of Bessel functions. Cambridge, 1958. | JFM 50.0264.01

G.N. Wart [48] Linearized theory of steady high-speed flow. Cambridge, 1955. | MR 67649 | Zbl 0064.43703

E.T. Whittaker and G.N. Watson [49] A course of modern analysis. Cambridge, 1958. | JFM 45.0433.02

W.E. Williams [50] The reduction of boundary value problems to Fredholm integral equations of the second kind. Z. Angew. Math. Phys. 13, 133-152 (1962). | Zbl 0123.29504

[51] Diffraction by a disk. Proc. Roy. Soc. Ser. A., 267, 77-87 (1962). | Zbl 0113.44402

[52] Electromagnetic diffraction by a circular disk. Proc. Cambridge Philos. Soc. 58, 625-630 (1962). | Zbl 0114.43502

R.J. Zwaan [53] Some comparative calculations with the lifting surface theory of Laschka for circular and elliptic wings oscillating in subsonic flow. Nat. Aero- and Astronaut. Res. Inst., Amsterdam, NLR Rep. F. 241 (1964).