Free Access
Issue
ESAIM: M2AN
Volume 28, Number 6, 1994
Page(s) 761 - 780
DOI https://doi.org/10.1051/m2an/1994280607611
Published online 31 January 2017
  1. O. M. RAYLEIGH, 1916, The Theory of Helmholtz Resonator, Proc. of Royal Soc., London, 92, 265-275. [Zbl: 46.1273.03] [JFM: 46.1273.03]
  2. J. M. MILES, 1971, Scattering by a Spherical Cap, Journ. Acoust. Soc. of America, 50, 892-903.
  3. R. R. GADYL'SHIN, 1990, On the amplitude of oscillations in Helmholtz resonator, Dokl. Akad. Nauk. SSSR, 310, 1094-1097. [MR: 1050165]
  4. R. R. GADYL'SHIN, 1992, Surface potentials and the method of matched asymptotic expansions in a problem of Helmholtz resonator, Algebra i Analiz, 4 88-115. [MR: 1182395] [Zbl: 0787.35024]
  5. P. D. LAX, R. S. PHILLIPS, 1967, Scattering Theory, Academic Press, New York. [MR: 217440] [Zbl: 0186.16301]
  6. J. SANCHEZ-HUBERT, E. SANCHEZ-PALENCIA, 1989, Vibration and Coupling of Continuons Systems. Asymptotic Methods, Berlin, Springer-Verlag. [MR: 996423] [Zbl: 0698.70003]
  7. R. R. GADYL'SHIN, 1992, The method of matched asymptotic expansions in the problem of acoustic Helmholtz resonator, Prikl. Mat. Mekh., 56, 412-418. [MR: 1191827] [Zbl: 0786.76075]
  8. [8]R. R. GADYL'SHIN, 1992, On influence of choice of location for hole and on its form to properties of acoustic resonator, Teor i mat. fiz., 93, 107-118. [MR: 1226213]
  9. R. R. GADYL'SHIN, 1992, About merged poles of an acoustic resonator, Doklady Akademii Nauk SSSR, 324, 773-776. [MR: 1201688]
  10. R. R. GADYL'SHIN, 1992, On system of inserted resonators, Doklady Akademii Nauk SSSR, 326, 939-942. [MR: 1202315] [Zbl: 0793.76079]
  11. R. R. GADYL'SHIN, On quasi-stationary state of Helmholtz resonator, Prikl. Mat. Mekh. (to appear)
  12. M. D. VAN DYKE, 1964, Perturbation Method in Fluid Mechanics, Academic Press, New York. [MR: 176702] [Zbl: 0136.45001]
  13. A. H. NAYFEH, 1973, Perturbation Methods, John Wiley, New York. [MR: 404788] [Zbl: 0265.35002]
  14. A. M. IL'IN, 1989, Matched asymptotic expansions for solutions of boundary valued problems, Nauka, Moscow. [MR: 1007834]
  15. J. T. BEALE, 1973, Scattering Frequencies of Resonators, Comm. Pure and Applied Math., 26, 549-564. [MR: 352730] [Zbl: 0254.35094]
  16. R. M. BROWN, P. D. HISLOP, A. MARTINEZ, Eigenvalues and resonances for domains with tube : Neumann boundary conditions, J. Differential equation (to appear). [MR: 1310941] [Zbl: 0815.35075]
  17. R. R. GADYL'SHIN, On poles of acoustic resonator, Funktsional. Anal. i Prilozhen. (to appear). [MR: 1264313]
  18. R. R. GADYL'SHIN, 1993, On scattering frequencies of acoustic resonator, C. R. Acad. Sci. Paris Sér. I, vol. 316, 859-963. [MR: 1218297] [Zbl: 0774.76071]
  19. S. JIMBO, Perturbation formula of eigenvalues in a singularly perturbed domain, J. Math. Soc., Japan (to appear). [MR: 1206658] [Zbl: 0785.35069]
  20. R. R. GADYL'SHIN, Asymptotic of second eigenfrequency for System of two body connected by thin tube, Teor. i mat. fiz. (to appear).
  21. D. COLTON, R. KRESS, 1983, Integral Equation Methods in Scattering Theory, John Willey & Sons, New York. [MR: 700400] [Zbl: 0522.35001]
  22. V. G. MAZ'YA, S. A. NAZAROV, B. A. PLAMENEVSKY, 1984, Asymptotical expansion of eigenvalues of boundary value problems for Laplacian, Izv. Akad. Nauk SSSR, Ser. mat., 48, 347-371. [MR: 740795] [Zbl: 0566.35031]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you