Geodesic
On scattering by cylinder with narrow slit and with shell of finite depth
Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 1, pp. 24-43 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The method of matching asymptotic expansions is applied to construction of asymptotics of poles for the Green function analytic continuation of a two-dimensional analog of Helmholtz resonator with a shell of a finite depth and with Neumann's boundary condition. The explicit formulae for the principle terms of asymptotics of poles, for corresponding generalized eigenfunctions and for solutions of scattering problem are obtained. 
@article{TMF_1996_106_1_a2,
     author = {R. R. Gadyl'shin},
     title = {On scattering by cylinder with narrow slit and with shell of finite depth},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {24--43},
     year = {1996},
     volume = {106},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_106_1_a2/}
}
TY  - JOUR
AU  - R. R. Gadyl'shin
TI  - On scattering by cylinder with narrow slit and with shell of finite depth
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 24
EP  - 43
VL  - 106
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_106_1_a2/
LA  - ru
ID  - TMF_1996_106_1_a2
ER  - 
%0 Journal Article
%A R. R. Gadyl'shin
%T On scattering by cylinder with narrow slit and with shell of finite depth
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 24-43
%V 106
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1996_106_1_a2/
%G ru
%F TMF_1996_106_1_a2
R. R. Gadyl'shin. On scattering by cylinder with narrow slit and with shell of finite depth. Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 1, pp. 24-43. http://geodesic.mathdoc.fr/item/TMF_1996_106_1_a2/

[1] Beale J. T., Commun. Pure and Appl. Math., 26:4 (1973), 549–564 | DOI | MR

[2] Lord Rayleigh, Proc. Roy. Soc. London. A, 92:638 (1916), 265–275 | DOI | MR | Zbl

[3] Hubert Palencia J., Sanchez Palencia E., Vibration and Coupling of Continuous Systems. Asymptotic Methods, Springer-Verlag, Berlin, 1989 | MR | Zbl

[4] Gadylshin R. R., Izv. RAN, ser. matem., 1993, no. 5, 44–74 | Zbl

[5] Gadyl'shin R. R., J. Math. Phys., 35:7 (1994), 3464–3481 | DOI | MR | Zbl

[6] Brown R. M., Hislop P. D., Martinez A., Eigenvalues and resonances for domains with tubes: Neumann boundary conditions, Research report 92-06, Univ. of Kentucky, 1992 | MR

[7] Gadyl'shin R. R., Compt. Rend. Acad. Sci. Série I, 316 (1993), 959–963 | MR | Zbl

[8] Gadylshin R. R., Funkts. analiz i ego prilozh., 27:4 (1993), 3–16 | MR | Zbl

[9] Van Daik M., Metody vozmuschenii v mekhanike zhidkosti, Mir, M., 1967 | Zbl

[10] Naife A. Kh., Metody vozmuschenii, Mir, M., 1986 | MR

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

[12] Sanches-Palensia E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984 | MR

[13] Gadylshin R. R., Diff. uravneniya, 30:2 (1994), 221–229 | MR | Zbl

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

[15] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[16] Gotlib V. Yu., Kagan B. A., Kivman G. A., Mor. gidrofiz. zhurnal, 1985, no. 5, 3–8

[17] Jimbo S., J. Diff. Equation, 77:2 (1989), 322–350 | DOI | MR | Zbl

[18] Fang Q., Hirosima Math. J., 20 (1990), 549–571 | MR | Zbl

[19] Hempel R., Seco L. A., Simon B., J. Funct. Annal., 102:2 (1991), 448–483 | DOI | MR | Zbl

[20] Jimbo S., Morita Y., Comm. Partial Diff. Equation, 17 (1992), 523–552 | MR | Zbl

[21] Kiselev A. A., Pavlov B. S., TMF, 100:3 (1994), 354–366 | MR | Zbl

[22] Jimbo S., J. Math. Soc. Japan, 45:2 (1993), 339–356 | DOI | MR | Zbl

[23] Gadylshin R. R., TMF, 97:1 (1993), 68–77 | MR | Zbl