@article{ZVMMF_1992_32_9_a9,
author = {R. R. Gadyl'shin},
title = {The {Helmholtz} resonator with a small aperture},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1464--1475},
year = {1992},
volume = {32},
number = {9},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_9_a9/}
}
R. R. Gadyl'shin. The Helmholtz resonator with a small aperture. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 9, pp. 1464-1475. http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_9_a9/
[1] Rayleigh O. M., “The theory of Gelmholtz resonator”, Proc. Roy. Soc. London A, 92:638 (1916), 265–275 | DOI | Zbl
[2] Shestopalov V. P., Summatornye uravneniya v sovremennoi teorii difraktsii, Nauk. dumka, Kiev, 1983 | MR
[3] Gotlib V. Yu., “Rasseyanie na kruglom rezonatore s uzkoi schelyu kak zadacha teorii vozmuschenii”, Dokl. AN SSSR, 287:5 (1986), 1109–1113 | MR
[4] Arsenev A. A., “Ob osobennostyakh analiticheskogo prodolzheniya i rezonansnykh svoistvakh resheniya zadachi rasseyaniya dlya uravneniya Gelmgoltsa”, Zh. vychisl. matem. i matem. fiz., 12:1 (1972), 112–138 | MR
[5] Sanches-Palensiya E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984, 472 pp. | MR
[6] Kondratev V. A., “O gladkosti resheniya zadachi Dirikhle dlya ellipticheskikh uravnenii vtorogo poryadka v kusochno-gladkoi oblasti”, Differents. ur-niya, 6:10 (1970), 1831–1843
[7] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. Mosk. matem. ob-va, 16, M., 1967, 209–292
[8] Mazya V. G., Plamenevskii B. A., “Ob ellipticheskikh kraevykh zadachakh v oblasti s kusochno-gladkoi granitsei”, Tr. simpoziuma po mekhan. sploshnoi sredy i rodstvennym probl. analiza, v. 1, Tbilisi, 1971, 171–181
[9] Gadylshin R. R., Poverkhnostnye potentsialy v zadache o rezonatore Gelmgoltsa, Dep. v VINITI, No 4476-V90, 1990, 24 pp.
[10] Polia G., Sege G., Izoperimetricheskie neravenstva v matematicheskoi fizike, Fizmatgiz, M., 1962
[11] Van-Daik M., Metody vozmuschenii v mekhanike zhidkosti, Mir, M., 1967
[12] Naife A., Metody vozmuschenii, Mir, M., 1976 | MR
[13] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR
[14] Gadylshin R. R., “Singulyarno vozmuschennaya zadacha dlya operatora Gelmgoltsa”, Differents. ur-niya s malym parametrom, Sverdlovsk, 1984, 19–35
[15] Gadylshin R. R., “Asimptotika sobstvennogo znacheniya singulyarno vozmuschennoi ellipticheskoi zadachi s malym parametrom v granichnom uslovii”, Differents. ur-niya, 22:4 (1986), 640–652 | MR
[16] Babich V. M., “Ob analiticheskom prodolzhenii rezolventy vneshnikh zadach dlya operatora Laplasa na vtoroi list”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, 3, Izd-vo KhGU, Kharkov, 1966, 151–157
[17] Ramm A. G., “O vneshnikh zadachakh difraktsii”, Radiotekhn. i elektronika, 17:7 (1972), 1362–1365
[18] Ilin A. M., “Kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka v oblasti s uzkoi schelyu. 2: Oblast s malym otverstiem”, Matem. sb., 103(145):2 (1977), 265–284 | MR