Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string

Behrouz Emamizadeh, Amin Farjudian

Research output: Journal PublicationArticlepeer-review

1 Citation (Scopus)
33 Downloads (Pure)

Abstract

In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will also provide further insight into the dynamics of the non-principal eigenvalues of the system.
Original languageEnglish
Pages (from-to)123-136
Number of pages14
JournalNonautonomous Dynamical Systems
Volume1
Issue number1
Early online date15 Aug 2014
DOIs
Publication statusPublished - 15 Aug 2014

Keywords

  • Derivative
  • Eigenvalue problem
  • Monotonicity
  • Ordinary differential equation
  • Principal eigenvalue
  • Symmetric rearrangements

ASJC Scopus subject areas

  • Applied Mathematics
  • Analysis
  • Statistics and Probability
  • Numerical Analysis

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