Geodesic
Green’s function for the Helmholtz equation in a polygonal domain of special form with ideal boundary conditions
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 150-167 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A formal approach for the construction of the Green's function in a polygonal domain with the Dirichlet boundary conditions is proposed. The complex form of the Kontorovich–Lebedev transform and reduction to a system of integral equations is exploited. The far-field asymptotics of the wave field is discussed. 
@article{ZNSL_2018_471_a10,
     author = {M. A. Lyalinov},
     title = {Green{\textquoteright}s function for the {Helmholtz} equation in a~polygonal domain of special form with ideal boundary conditions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--167},
     year = {2018},
     volume = {471},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a10/}
}
TY  - JOUR
AU  - M. A. Lyalinov
TI  - Green’s function for the Helmholtz equation in a polygonal domain of special form with ideal boundary conditions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 150
EP  - 167
VL  - 471
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a10/
LA  - ru
ID  - ZNSL_2018_471_a10
ER  - 
%0 Journal Article
%A M. A. Lyalinov
%T Green’s function for the Helmholtz equation in a polygonal domain of special form with ideal boundary conditions
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 150-167
%V 471
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a10/
%G ru
%F ZNSL_2018_471_a10
M. A. Lyalinov. Green’s function for the Helmholtz equation in a polygonal domain of special form with ideal boundary conditions. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 150-167. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a10/

[1] V. M. Babich, M. A. Lyalinov, V. E. Grikurov, Diffraction Theory. The Sommerfeld-Malyuzhinets Technique, Alpha Sci. Ser. Wave Phenom., Alpha Science, Oxford, 2008

[2] M. A. Lyalinov, N. Y. Zhu, Scattering of Waves by Wedges and Cones with Impedance Boundary Conditions, Mario Boella Series on Electromagnetism in Information Communication, SciTech-IET, Edison, NJ, 2012

[3] J.-M. L. Bernard, “A spectral approach for scattering by impedance polygons”, Q. J. Mech. Appl. Math., 59:4 (2006), 517–550 | DOI | MR | Zbl

[4] M. A. Lyalinov, “Integral equations and the scattering diagram in the problem of diffraction by two contacting wedges with polygonal boundary”, J. Math. Sci., 214:3 (2016), 322–336 | DOI | MR | Zbl

[5] D. S. Jones, “The Kontorovich-Lebedev transform”, J. Inst. Maths Appl., 26 (1980), 133–141 | DOI | MR | Zbl

[6] A. D. Avdeev, S. M. Grudskii, “O modifitsirovannom preobrazovanii Kontorovicha-Lebedeva i ego prilozhenii k zadache difraktsii tsilindricheskoi volny na idealno provodyaschem kline”, Radiotekhnika i elektronika, 39:7 (1994), 1081–1089

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

[8] I. S. Gradstein, I. M. Ryzhik, Tables of Integrals, Series and Products, 4th ed., Academic Press, Orlando, 1980 | MR

[9] L. S. Rakovschik, “Sistemy integralnykh uranenii s pochti raznostnymi operatorami”, Sibirskii Mat. Zhurnal, 3:2 (1962), 250–255