Geodesic
Characteristic frequencies of bodies with thin spikes.~III. Frequency splitting
Matematičeskie zametki, Tome 61 (1997) no. 4, pp. 494-502.

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

The eigenvalue problem for the Laplace operator with the Neumann boundary conditions in a domain that has a thin spike of finite length is considered for the case in which the limit value is an eigenvalue both for the main body and the spike. The method of matched asymptotic expansions is used to construct total asymptotics of the eigenvalues of the perturbed problem and obtain closed formulas for the leading asymptotic terms. 
@article{MZM_1997_61_4_a1,
     author = {R. R. Gadyl'shin},
     title = {Characteristic frequencies of bodies with thin {spikes.~III.} {Frequency} splitting},
     journal = {Matemati\v{c}eskie zametki},
     pages = {494--502},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a1/}
}
TY  - JOUR
AU  - R. R. Gadyl'shin
TI  - Characteristic frequencies of bodies with thin spikes.~III. Frequency splitting
JO  - Matematičeskie zametki
PY  - 1997
SP  - 494
EP  - 502
VL  - 61
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a1/
LA  - ru
ID  - MZM_1997_61_4_a1
ER  - 
%0 Journal Article
%A R. R. Gadyl'shin
%T Characteristic frequencies of bodies with thin spikes.~III. Frequency splitting
%J Matematičeskie zametki
%D 1997
%P 494-502
%V 61
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a1/
%G ru
%F MZM_1997_61_4_a1
R. R. Gadyl'shin. Characteristic frequencies of bodies with thin spikes.~III. Frequency splitting. Matematičeskie zametki, Tome 61 (1997) no. 4, pp. 494-502. http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a1/

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

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

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

[4] Naife A., Metody vozmuschenii, Mir, M., 1976

[5] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989

[6] Mazya V. G., Nazarov S. A., Plamenevskii B. A., “Asimptoticheskie razlozheniya sobstvennykh chisel kraevykh zadach dlya operatora Laplasa v oblastyakh s malymi otverstiyami”, Izv. AN SSSR. Ser. matem., 48:2 (1984), 347–371 | MR