Estimates for Resonant Frequencies Under Boundary Deformation in Multi-dimensional Space

Authors

  • Abdessatar Khelifi University of Bizerte
  • Mohammed Nour Shamma Al Gassim University

Keywords:

Resonant frequencies, Boundary integral equation, Error estimates

Abstract

In multi-dimensional space, we address the
integral equation method to investigate the interplay between the geometry, boundary conditions and the properties of the resonant
frequencies and their associated eigenfunctions under boundary variations of domain. We provide a rigorous derivation of asymptotic
expansions for eigenfunctions and we establish error estimations for both resonant frequencies and eigenfunctions of the Helmholtz
eigenvalue problem.

Author Biography

  • Abdessatar Khelifi, University of Bizerte

    Zarzouna, Bizerte.

    7021 Bizerte.

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Published

2010-04-09

Issue

Vol. 3 No. 2: (April 2010)

Section

Mathematical Analysis

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Estimates for Resonant Frequencies Under Boundary Deformation in Multi-dimensional Space. (2010). European Journal of Pure and Applied Mathematics, 3(2), 282-294. https://ejpam.com/index.php/ejpam/article/view/323