Geodesic
On diffraction of a plane wave by an impedance cone
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 191-215 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Some questions on substantiation of the solution in the diffraction problem by an impedance cone are discussed. The surface waves as well as the Weyl–van-der-Pol phenomenon are studied in the zone illuminated by the reflected rays. 
@article{ZNSL_2003_297_a11,
     author = {M. A. Lyalinov},
     title = {On diffraction of a~plane wave by an impedance cone},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {191--215},
     year = {2003},
     volume = {297},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a11/}
}
TY  - JOUR
AU  - M. A. Lyalinov
TI  - On diffraction of a plane wave by an impedance cone
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 191
EP  - 215
VL  - 297
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a11/
LA  - ru
ID  - ZNSL_2003_297_a11
ER  - 
%0 Journal Article
%A M. A. Lyalinov
%T On diffraction of a plane wave by an impedance cone
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 191-215
%V 297
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a11/
%G ru
%F ZNSL_2003_297_a11
M. A. Lyalinov. On diffraction of a plane wave by an impedance cone. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 191-215. http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a11/

[1] V. A. Borovikov, Difraktsiya na mnogougolnikakh i mnogogrannikakh, Nauka, Moskva, 1966 | MR

[2] V. M. Babich, D. B. Dement'ev, B. A. Samokish, V. P. Smyshlyaev, “On evaluation of the diffraction coefficients for arbitrary “non-singular” directions of a smooth convex cone”, SIAM Appl. Math., 60:2 (2000), 536–573 | DOI | MR | Zbl

[3] D. S. Jones, “Scattering by a cone”, Q. J. Mech. Appl. Math., 50 (1997), 499–523 | DOI | MR | Zbl

[4] J. M. L. Bernard, Rapport CEA-R-5764, Editions Dist-Saclay, CEA/Saclay, 1997

[5] J. M. L. Bernard, M. A. Lyalinov, “The leading asymptotic term for the scattering diagram in the problem of diffraction by a narrow circular impedance cone”, J. Phys. A, 32:4 (1999), L43–L48 | DOI | MR | Zbl

[6] J. M. L. Bernard, M. A. Lyalinov, “Spectral domain solution and asymptotics for the diffraction by an impedance cone”, IEEE Trans Anten. Propag., 49:12 (2001), 1633–1635 | DOI | MR

[7] L. B. Felsen, “Plane wave scattering by small angle cones”, IRE Trans. Antennas Propag., 50 (1957), 121–129 | DOI

[8] V. M. Babich, “O difraktsii vysokochastotnoi akusticheskoi volny na absolyutno zhestkom konuse proizvolnogo secheniya”, Prikl. Matem. i Mekhan., 60:1 (1996), 72–78 | MR | Zbl

[9] J. M. L. Bernard, M. A. Lyalinov, “Diffraction of scalar waves by a convex impedance cone of arbitrary cross-section”, Wave Motion, 33 (2001), 155–181 | DOI | MR | Zbl

[10] J. M. L. Bernard, M. A. Lyalinov, “Electromagnetic scattering by an impedance cone”, IMA Journ. on Appl. Math., 2002 (to appear)

[11] Y. A. Antipov, “Diffraction of a plane wave by a circular cone with an impedance boundary condition”, SIAM Journ. Appl. Math., 62:4 (2002), 1122–1152 | DOI | MR | Zbl

[12] J. M. L. Bernard, M. A. Lyalinov, “On diffraction by an impedance cone of an arbitrary cross section: the far field in the penumbral zone”, Proc. of Intern. Workshop on Direct and Inverse Wave Scattering (Gebze, Turkey, Sept. 25–29, 2002), 73–82

[13] V. Kamotski, G. Lebeau, “Diffraction by an elastic wedge with stress-free boundary: existence and uniqueness”, Proc. Royal. Soc. London (to appear)

[14] V. A. Fok, Problemy difraktsii i rasprostraneniya voln, M., 1970

[15] I. M. Ryzhik, I. S. Gradshtein, Tablitsy integralov, summ i proizvedenii, GTTL., M.-L., 1951

[16] D. S. Jones, The theory of electromagnetizm, Pergamon Press, London, 1964 | Zbl

[17] G. D. Maliuzhinets, “Excitation, reflection and emission of surface waves from a wedge with given face impedances”, Sov. Phys. Dokl., 3 (1958), 752–755

[18] A. A. Tuzhilin, “K teorii neodnorodnykh funktsionalnykh uravnenii Malyuzhintsa”, Differentsialnye uravneniya, 9:11 (1973), 2058–2064 | MR

[19] M. V. Fedoryuk, Asimptotika: integraly i ryady, Nauka, Moskva, 1987 | MR