Asymptotics of scattering frequencies with small imaginary parts for an acoustic resonator

Rustem R. Gadyl'shin

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 6, page 761-780
  • ISSN: 0764-583X

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Gadyl'shin, Rustem R.. "Asymptotics of scattering frequencies with small imaginary parts for an acoustic resonator." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.6 (1994): 761-780. <http://eudml.org/doc/193759>.

@article{Gadylshin1994,
author = {Gadyl'shin, Rustem R.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {thin connecting tube; shell; Neumann boundary condition; power series; small parameter},
language = {eng},
number = {6},
pages = {761-780},
publisher = {Dunod},
title = {Asymptotics of scattering frequencies with small imaginary parts for an acoustic resonator},
url = {http://eudml.org/doc/193759},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Gadyl'shin, Rustem R.
TI - Asymptotics of scattering frequencies with small imaginary parts for an acoustic resonator
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 6
SP - 761
EP - 780
LA - eng
KW - thin connecting tube; shell; Neumann boundary condition; power series; small parameter
UR - http://eudml.org/doc/193759
ER -

References

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  3. [3] R. R. GADYL'SHIN, 1990, On the amplitude of oscillations in Helmholtz resonator, Dokl. Akad. Nauk. SSSR, 310, 1094-1097. MR1050165
  4. [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. Zbl0787.35024MR1182395
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  6. [6] J. SANCHEZ-HUBERT, E. SANCHEZ-PALENCIA, 1989, Vibration and Coupling of Continuons Systems. Asymptotic Methods, Berlin, Springer-Verlag. Zbl0698.70003MR996423
  7. [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. Zbl0786.76075MR1191827
  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. MR1226213
  9. [9] R. R. GADYL'SHIN, 1992, About merged poles of an acoustic resonator, Doklady Akademii Nauk SSSR, 324, 773-776. MR1201688
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  12. [12] M. D. VAN DYKE, 1964, Perturbation Method in Fluid Mechanics, Academic Press, New York. Zbl0136.45001MR176702
  13. [13] A. H. NAYFEH, 1973, Perturbation Methods, John Wiley, New York. Zbl0265.35002MR404788
  14. [14] A. M. IL'IN, 1989, Matched asymptotic expansions for solutions of boundary valued problems, Nauka, Moscow. MR1007834
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  17. [17] R. R. GADYL'SHIN, On poles of acoustic resonator, Funktsional. Anal. i Prilozhen. (to appear). MR1264313
  18. [18] R. R. GADYL'SHIN, 1993, On scattering frequencies of acoustic resonator, C. R. Acad. Sci. Paris Sér. I, vol. 316, 859-963. Zbl0774.76071MR1218297
  19. [19] S. JIMBO, Perturbation formula of eigenvalues in a singularly perturbed domain, J. Math. Soc., Japan (to appear). Zbl0785.35069MR1206658
  20. [20] R. R. GADYL'SHIN, Asymptotic of second eigenfrequency for System of two body connected by thin tube, Teor. i mat. fiz. (to appear). 
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