Diffraction of plane wave by a transparent wedge: Sommerfeld–Malyuzhinets approach
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 37, Tome 354 (2008), pp. 157-172
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We consider a time-harmonic diffraction of a plane wave by a transparent wedge of an arbitrary opening by the Sommerfeld–Malyuzhinets approach, see, e.g., [1]. The wave propagation velocity inside the wedge and outside are equal. An explicit solution is presented, which is studied asymptotically as $kr\to\infty$ and $kr\to0$. Bibl. – 4 titles, fig. – 6.
@article{ZNSL_2008_354_a7,
author = {A. A. Matskovskii},
title = {Diffraction of plane wave by a~transparent wedge: {Sommerfeld{\textendash}Malyuzhinets} approach},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {157--172},
year = {2008},
volume = {354},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a7/}
}
A. A. Matskovskii. Diffraction of plane wave by a transparent wedge: Sommerfeld–Malyuzhinets approach. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 37, Tome 354 (2008), pp. 157-172. http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a7/
[1] V. M. Babich, M. A. Lyalinov, V. E. Grikurov, Metod Zommerfelda–Malyuzhintsa v zadachakh difraktsii, S.-Peterburg, 2003
[2] V. I. Smirnov, Kurs vysshei matematiki, T. IV, Ch. II, Gostekhizdat, M., L., 1951
[3] J.-P. Croisille, G. Lebeau, Diffraction by an immersed elastic wedge, Lect. Notes Math., 1723, Springer, 1999 | MR | Zbl
[4] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989 | MR | Zbl