Solution of the Dirichlet problem for the Helmholtz equation in domains with a rough boundary
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2006), pp. 43-49.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{IVM_2006_9_a6,
     author = {E. K. Lipachev},
     title = {Solution of the {Dirichlet} problem for the {Helmholtz} equation in domains with a rough boundary},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {43--49},
     publisher = {mathdoc},
     number = {9},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2006_9_a6/}
}
TY  - JOUR
AU  - E. K. Lipachev
TI  - Solution of the Dirichlet problem for the Helmholtz equation in domains with a rough boundary
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2006
SP  - 43
EP  - 49
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2006_9_a6/
LA  - ru
ID  - IVM_2006_9_a6
ER  - 
%0 Journal Article
%A E. K. Lipachev
%T Solution of the Dirichlet problem for the Helmholtz equation in domains with a rough boundary
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2006
%P 43-49
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2006_9_a6/
%G ru
%F IVM_2006_9_a6
E. K. Lipachev. Solution of the Dirichlet problem for the Helmholtz equation in domains with a rough boundary. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2006), pp. 43-49. http://geodesic.mathdoc.fr/item/IVM_2006_9_a6/

[1] Brekhovskikh L. M., “Difraktsiya zvukovykh voln na nerovnoi poverkhnosti”, DAN SSSR, 79:4 (1951), 585–588

[2] Brekhovskikh L. M., “Difraktsiya elektromagnitnykh voln na nerovnoi poverkhnosti”, DAN SSSR, 81:6 (1951), 1023–1026

[3] Strett Dzh. V. (Relei), Teoriya zvuka, T. 2, Gostekhizdat, M., 1955, 476 pp.

[4] Brekhovskikh L. M., Lysanov Yu. P., Teoreticheskie osnovy akustiki okeana, Gidrometeoizdat, L., 1982, 264 pp.

[5] Bass F. G., Fuks I. M., Rasseyanie voln na statisticheski nerovnoi poverkhnosti, Nauka, M., 1972, 424 pp. | MR

[6] Bass F. G., Krutin Yu. I., Sirenko Yu. K. i dr., “Vozmozhnost strogogo rascheta rasseyannykh proizvolnymi i sluchainymi poverkhnostyami polei s ispolzovaniem algoritmov metoda analiticheskoi regulyarizatsii”, Elektromagnitnye volny i elektronnye sistemy, 2:1 (1997), 5–17 | MR

[7] Zhang B., Chandler-Wilde S. N., “Integral equation methods for scattering by infinite rough surfaces”, Math. Meth. Appl. Sci., 26 (2003), 463–488 | DOI | MR | Zbl

[8] Tsang L., Kong J. A., Ding K. H., Scattering of electromagnetic waves: theories and applications, Wiley-Interscience, New York, 2000, 426 pp. | Zbl

[9] Tumakov D. N., “Integralnoe uravnenie zadachi difraktsii elektromagnitnoi volny na krivolineinom metallicheskom ekrane”, Tr. Matem. tsentra im. N. I. Lobachevskogo, 13, Izd-vo “DAS”, Kazan, 2001, 218–225

[10] Lipachev E. K., “K priblizhennomu resheniyu kraevoi zadachi difraktsii voln na oblastyakh s beskonechnoi granitsei”, Izv. vuzov. Matematika, 2001, no. 4, 69–72 | MR | Zbl

[11] Kolton D., Kress R., Metody integralnykh uravnenii v teorii rasseyaniya, Mir, M., 1987, 311 pp. | MR

[12] Mazya V. G., “Granichnye integralnye uravneniya”, Itogi nauki i tekhniki. Sovr. probl. matem. Fundam. napr., 27, VINITI AN SSSR, M., 1988, 131–228 | MR

[13] Gabdulkhaev B. G., Optimalnye approksimatsii reshenii lineinykh zadach, Izd-vo Kazansk. un-ta, Kazan, 1980, 232 pp. | MR

[14] Vaganov R. B., Katsenelenbaum B. Z., Osnovy teorii difraktsii, Nauka, M., 1982, 272 pp. | MR | Zbl

[15] Pleschinskii N. B., Uravnenie Gelmgoltsa v poluploskosti i skalyarnye zadachi difraktsii elektromagnitnykh voln na ploskikh metallicheskikh ekranakh, Preprint PMF-03–02, Kazansk. matem. o-vo, Kazan, 2003, 30 pp.

[16] Ilinskii A. S., Kravtsov V. V., Sveshnikov A. G., Matematicheskie modeli elektrodinamiki, Vyssh. shkola, M., 1991, 224 pp.

[17] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977, 736 pp.

[18] Ilinskii A. S., Shestopalov Yu. V., Primenenie metodov spektralnoi teorii v zadachakh rasprostraneniya voln, Izd-vo MGU, M., 1989, 184 pp.

[19] Shestopalov Yu. V., “Primenenie metoda obobschennykh potentsialov dlya resheniya nekotorykh zadach teorii difraktsii i rasprostraneniya voln”, Zhurn. vychisl. matem. i matem. fiz., 1990, no. 7, 1081–1092 | MR

[20] Abramovits M., Stigan I., Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979, 832 pp. | MR

[21] Gabdulkhaev B. G., “Approksimatsiya polinomami i splainami reshenii slabo singulyarnykh integralnykh uravnenii”, Teoriya priblizheniya funktsii, Nauka, M., 1977, 89–93 | MR