Skip to main content
SpringerLink
Log in

On eigenfrequencies of bodies with thin branches. II. Asymptotics

  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. R. R. Gadyl'shin,On eigenfrequencies of bodies with thin branches. I.Convergence and bounds, Mat. Zametki.54 (1993), no. 5.

    Google Scholar 

  2. M. Van Dyke,Perturbation Methods in Mechanics of Fluids, Mir, Moscow, 1967.

    Google Scholar 

  3. A. Naife,Perturbation Methods, Mir, Moscow, 1976.

    Google Scholar 

  4. A. M. Il'in,Agreement of Asymptotic Expansions of Solutions of Boundary Value Problems, Nauka, Moscow, 1989.

    Google Scholar 

  5. V. G. Mazia, S. A. Nazarov, and B. A. Plamenevskii,Asymptotic expansions of eigenvalues of boundary value problems for Laplace operators in domains with small holes, Izv. Akad. Nauk SSSR, Ser. Mat.48 (1984), no. 2, 347–371.

    Google Scholar 

  6. R. R. Gadyl'shin,Splitting of multiple eigenvalue of the Dirichlet problem for the Laplace operator under singular perturbation of boundary condition, Mat. Zametki52 (1992), no. 4, 42–55.

    Google Scholar 

  7. R. R. Gadyl'shin,Asymptotics of eigenvalues of singular perturbed elliptic problem with small parameter under boundary condition, Diff. Uravneniya.22 (1986), no. 4, 640–652.

    Google Scholar 

  8. J. T. Beale,Scattering frequencies of resonators, Commun. Pure Appl. Math.26 (1973), no. 4, 549–564.

    Google Scholar 

  9. R. R. Gadyl'shin,On scattering frequencies of acoustic resonator, Preprint: Bashkirian Scientific Center of Ural Branch of Russian Academy of Sciences, Ufa, 1992.

    Google Scholar 

  10. P. Laks and R. Phillips,Scattering Theory, Mir, Moscow, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute and Computer Center, Ural Branch of the Russian Academy of Sciences, Ufa

    R. R. Gadyl'shin

Authors
  1. R. R. Gadyl'shin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 55, No. 1, pp. 20–34, January, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gadyl'shin, R.R. On eigenfrequencies of bodies with thin branches. II. Asymptotics. Math Notes 55, 14–23 (1994). https://doi.org/10.1007/BF02110759

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02110759

Keywords

Search

Navigation