Geodesic
Short wave point source near a unhomogenous halfplane
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 107-120 
A. A. Matskovskiy. Short wave point source near a unhomogenous halfplane. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 107-120. http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a6/
@article{ZNSL_2012_409_a6,
     author = {A. A. Matskovskiy},
     title = {Short wave point source near a~unhomogenous halfplane},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {107--120},
     year = {2012},
     volume = {409},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the diffraction of waves produced by a point source by unhomogenous halfplane. The square of wave-number inside unhomogenous region is supposed to decrease lineary with increasing the distance from the devision boundary. The main aim of the article is to obtain the asymptotic of a whispering gallery waves as $k\to\infty$, where $k$ is the wave-number in a homogenous region.

[1] V. M. Babich, V. S. Buldyrev, Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972 | MR

[2] V. S. Buldyrev, “Interferentsiya korotkikh voln v zadache difraktsii na neodnorodnom tsilindre proizvolnogo secheniya”, IVUZ. Radiofizika, 10:5 (1967), 699–711

[3] V. M. Babich, N. Ya. Kirpichnikova, Metod pogranichnogo sloya v zadachakh difraktsii, LGU, 1974 | MR

[4] V. M. Babich, “On asymptotics of a wave field near the origin of an interference head wave”, Electromagnetics in Advanced Applications, 2007, 704–705

[5] V. B. Philippov, “Point source field near concave boundary”, Zap. Nauchn. Semin. POMI, 354, 2008, 212–219 | Zbl

[6] V. S. Buldyrev, “Issledovanie funktsii Grina v zadache difraktsii na prozrachnom krugovom tsilindre. I”, Zh. vychisl. matem. fiz., 4, dop. k No 4 (1964), 275–286 | MR | Zbl

[7] V. M. Babich, “Boundary layer approach to construct an interference head wave”, Days on Diffraction, 2007, 19–21