Geodesic
Waves produced by sources on expanding disk
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 38-47 
V. V. Borisov. Waves produced by sources on expanding disk. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 38-47. http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a2/
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     author = {V. V. Borisov},
     title = {Waves produced by sources on expanding disk},
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     pages = {38--47},
     year = {2006},
     volume = {332},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The explicit solutions of the inhomogeneous wave equation are constructed. The solutions obtained describe waves generated by a source distribution of a disk that expands with velocities less, equal, or greater than the wave-front velocity. The structure and directional transmission waves are discussed. Possibility of an application of the scalar solutions to electromagnetic waves is shown. Bibliography: 8 titles.

[1] V. V. Borisov, Elektromagnitnye polya neustanovivshikhsya tokov, SPbGU, S.-Peterburg, 1996, 207 pp.

[2] V. V. Borisov, I. I. Simonenko, “Electromagnetic fields produced by sources on a spherical wavefront”, Eur. Phys. J. B, 1:1 (2000), 85–93 | DOI

[3] V. I. Smirnov, “Reshenie predelnoi zadachi dlya volnovogo uravneniya v sluchae kruga i sfery”, Dokl. AN SSSR, 1937, no. 14, 13–16

[4] H. M. Macdonald, “Note on evalution of a certain integral containing Bessel's finctions”, Proc. of London Math. Soc. Ser. 2, 7 (1909), 142–149 | DOI | Zbl

[5] J. H. Brittingham, “Focus wave modes in homogeneous Maxwell's equation: transverse electric modes”, J. Appl. Phys., 54:5 (1983), 1179–1189 | DOI

[6] A. A. Vlasov, Teoriya mnogikh chastits, GITTL, M.-L., 1950, 346 pp.

[7] A. A. Vlasov, Statisticheskaya funktsiya raspredeleniya, Nauka, FM, M., 1966, 355 pp. | MR | Zbl

[8] V. V. Borisov, “Spherical-harmonic representation of transient waves produced by sources on a superluminal expanding sphere”, Day on Diffraction-01, St.Petersburg, 2001, 38–40