Asymptotic expansion of the solutions of a singularly perturbed Dirichlet problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 36 (1996) no. 1, pp. 92-102 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_1996_36_1_a5,
     author = {R. R. Gadyl'shin},
     title = {Asymptotic expansion of the solutions of a singularly perturbed {Dirichlet} problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {92--102},
     year = {1996},
     volume = {36},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_1_a5/}
}
TY  - JOUR
AU  - R. R. Gadyl'shin
TI  - Asymptotic expansion of the solutions of a singularly perturbed Dirichlet problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1996
SP  - 92
EP  - 102
VL  - 36
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_1_a5/
LA  - ru
ID  - ZVMMF_1996_36_1_a5
ER  - 
%0 Journal Article
%A R. R. Gadyl'shin
%T Asymptotic expansion of the solutions of a singularly perturbed Dirichlet problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1996
%P 92-102
%V 36
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_1_a5/
%G ru
%F ZVMMF_1996_36_1_a5
R. R. Gadyl'shin. Asymptotic expansion of the solutions of a singularly perturbed Dirichlet problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 36 (1996) no. 1, pp. 92-102. http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_1_a5/

[1] 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

[2] Beale J. T., “Scattering frequencies of resonators”, Communs. Pure and Appl. Math., 26:4 (1973), 549–564 | DOI | MR

[3] Petras S. V., “O rasscheplenii serii rezonansov na «nefizicheskom liste»”, Zap. nauchn. seminara LOMI, 51, L., 1975, 155–169 | MR | Zbl

[4] Sanches-Palensiya E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984, 472 pp. | MR

[5] Fernandéz C., “Resonances in scattering by a resonator”, Indiana Univ. Math. J., 34:1 (1985), 115–125 | DOI | MR | Zbl

[6] Hislop P. D., Martinez A., “Scattering resonances of Helmholtz resonator”, Indiana Univ. Math. J., 40:2 (1991), 767–788 | DOI | MR | Zbl

[7] Van-Daik M., Metody vozmuschenii v mekhanike zhidkosti, Mir, M., 1967

[8] Naife A., Metody vozmuschenii, Mir, M., 1976 | MR

[9] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[10] Gadylshin P. P., “O sobstvennykh chastotakh tel s tonkimi otrostkami. I: Skhodimost i otsenki”, Matem. zametki, 54:6 (1993), 10–21 | MR

[11] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973 | MR

[12] Gadylshin P. P., “Poverkhnostnye potentsialy i metod soglasovaniya asimptoticheskikh razlozhenii v zadache o rezonatore Gelmgoltsa”, Algebra i analiz, 4:2 (1992), 88–115 | MR

[13] Gadylshin P. P., “O sobstvennykh chastotakh tel s tonkimi otrostkami. II: Asimptotiki”, Matem. zametki, 55:1 (1994), 20–34 | MR

[14] Gadylshin P. P., “Metod sraschivaniya asimptoticheskikh razlozhenii v zadache ob akusticheskom rezonatore Gelmgoltsa”, Prikl. matem. i mekhan., 56:3 (1992), 412–418 | MR | Zbl

[15] Gadylshin P. P., “Rezonator Gelmgoltsa s malym otverstiem”, Zh. vychisl. matem. i matem. fiz., 32:9 (1992), 1464–1475 | MR

[16] Gadylshin P. P., “O polyusakh akusticheskogo rezonatora”, Funktsionalnyi analiz i ego prilozh., 27:4 (1993), 3–16 | MR

[17] Gadyl'shin R. R., “On scattering frequencies of acoustic resonator”, C.r. Acad. Sci. Série I., 316 (1993), 959–963 | MR

[18] Gadylshin P. P., “Dvumernyi analog rezonatora Gelmgoltsa s idealno zhestkimi stenkami”, Differents. ur-niya, 30:2 (1994), 221–229 | MR

[19] Gadyl'shin R. R., “On acoustic Helmholtz resonator and on its electromagnetic analogue”, J. Math. Phys., 35:7 (1994), 3464–3481 | DOI | MR