Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string
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 r...
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| Format: | Article |
| Language: | English |
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De Gruyter
2014
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| Online Access: | https://eprints.nottingham.ac.uk/56192/ |
| _version_ | 1848799290312359936 |
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| author | Emamizadeh, Behrouz Farjudian, Amin |
| author_facet | Emamizadeh, Behrouz Farjudian, Amin |
| author_sort | Emamizadeh, Behrouz |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:33:19Z |
| format | Article |
| id | nottingham-56192 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:33:19Z |
| publishDate | 2014 |
| publisher | De Gruyter |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-561922019-02-28T09:00:31Z https://eprints.nottingham.ac.uk/56192/ Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string Emamizadeh, Behrouz Farjudian, Amin 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. De Gruyter 2014-08-15 Article PeerReviewed application/pdf en cc_by_nc_nd https://eprints.nottingham.ac.uk/56192/2/2014-Emamizadeh_Farjudian-Monotonicity_Principal_Eigenvalue-DeGruyter-Format.pdf Emamizadeh, Behrouz and Farjudian, Amin (2014) Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string. Nonautonomous Dynamical Systems, 1 (1). pp. 123-136. ISSN 2353-0626 Eigenvalue problem; Ordinary differential equation; Principal eigenvalue; Monotonicity; Derivative; Symmetric rearrangements https://www.degruyter.com/dg/viewarticle/j$002fmsds.2014.1.issue-1$002fmsds-2014-0007$002fmsds-2014-0007.xml https://doi.org/10.2478/msds-2014-0007 https://doi.org/10.2478/msds-2014-0007 |
| spellingShingle | Eigenvalue problem; Ordinary differential equation; Principal eigenvalue; Monotonicity; Derivative; Symmetric rearrangements Emamizadeh, Behrouz Farjudian, Amin Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string |
| title | Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string |
| title_full | Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string |
| title_fullStr | Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string |
| title_full_unstemmed | Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string |
| title_short | Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string |
| title_sort | monotonicity of the principal eigenvalue related to a non-isotropic vibrating string |
| topic | Eigenvalue problem; Ordinary differential equation; Principal eigenvalue; Monotonicity; Derivative; Symmetric rearrangements |
| url | https://eprints.nottingham.ac.uk/56192/ https://eprints.nottingham.ac.uk/56192/ https://eprints.nottingham.ac.uk/56192/ |