Skip to main content
SpringerLink
Log in

Eigenfrequencies and eigenfunctions of the Laplacian for Neumann boundary conditions in a system of two coupled cavities

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

A model Laplacian with Neumann boundary conditions (Neumann problem) in a system of two cavities joined by a thin channel is investigated. An expression is obtained for the resolvent and also the first terms in the asymptotic expansions of the eigenvalues and eigenfunctions with respect to the small coupling parameter.

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

Similar content being viewed by others

References

  1. N. N. Voitovich, B. Z. Kantselenbaum, and A. N. Sivov,Generalized Method of Normal Oscillations in the Theory of Diffraction [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. R. Hempel, L. A. Seco, and B. Simon,J. Funct. Anal.,102, 448 (1991).

    Google Scholar 

  3. B. S. Pavlov and I. Yu. Popov,Vestn. Leningr. Univ., No. 4, 99 (1985).

    Google Scholar 

  4. B. A. Dubrovich, S. P. Novikov, and A. T. Fomenko,Modern Geometry [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. B. S. Pavlov,Usp. Mat. Nauk,42, 99 (1987).

    Google Scholar 

  6. B. S. Pavlov and I. Yu. Popov,Vestn. Leningr. Univ., No. 13, 116 (1984).

    Google Scholar 

  7. R. M. Brown, P. D. Hislop, and A. Martinez, “Eigenvalues and resonances for domains with tubes: Neumann boundary conditions,” Research Report. 92-06, University of Kentucky.

Download references

Authors
  1. A. A. Kiselev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. S. Pavlov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

State University, St. Petersburg. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 3, pp. 354–366, August, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kiselev, A.A., Pavlov, B.S. Eigenfrequencies and eigenfunctions of the Laplacian for Neumann boundary conditions in a system of two coupled cavities. Theor Math Phys 100, 1065–1074 (1994). https://doi.org/10.1007/BF01018571

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01018571

Keywords

Search

Navigation