An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients
This paper explores an operative technique for deriving nonlinear stability by studying double-diffusive porous convection with a concentration-based internal heat source. Previous stability analyses on this problem have yielded regions of potential subcritical instabilities where the linear instabi...
| Main Authors: | , |
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| Format: | Article |
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Royal Society
2012
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| Online Access: | https://eprints.nottingham.ac.uk/2968/ |
| _version_ | 1848790919874084864 |
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| author | Hill, Antony A. Malashetty, M.S. |
| author_facet | Hill, Antony A. Malashetty, M.S. |
| author_sort | Hill, Antony A. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This paper explores an operative technique for deriving nonlinear stability by studying double-diffusive porous convection with a concentration-based internal heat source. Previous stability analyses on this problem have yielded regions of potential subcritical instabilities where the linear instability and nonlinear stability thresholds do not coincide. It is shown in this paper that the operative technique yields sharp conditional nonlinear stability in regions where the instability is found to be monotonic. This is the first instance, in the present literature, where this technique has been shown to generate sharp thresholds for a system with spatially dependent coefficients, which strongly advocates its wider use. |
| first_indexed | 2025-11-14T18:20:16Z |
| format | Article |
| id | nottingham-2968 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:20:16Z |
| publishDate | 2012 |
| publisher | Royal Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-29682020-05-04T16:32:38Z https://eprints.nottingham.ac.uk/2968/ An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients Hill, Antony A. Malashetty, M.S. This paper explores an operative technique for deriving nonlinear stability by studying double-diffusive porous convection with a concentration-based internal heat source. Previous stability analyses on this problem have yielded regions of potential subcritical instabilities where the linear instability and nonlinear stability thresholds do not coincide. It is shown in this paper that the operative technique yields sharp conditional nonlinear stability in regions where the instability is found to be monotonic. This is the first instance, in the present literature, where this technique has been shown to generate sharp thresholds for a system with spatially dependent coefficients, which strongly advocates its wider use. Royal Society 2012-02-08 Article PeerReviewed Hill, Antony A. and Malashetty, M.S. (2012) An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468 (2138). pp. 323-336. ISSN 1471-2946 http://rspa.royalsocietypublishing.org/content/468/2138/323 doi:10.1098/rspa.2011.0137 doi:10.1098/rspa.2011.0137 |
| spellingShingle | Hill, Antony A. Malashetty, M.S. An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients |
| title | An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients |
| title_full | An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients |
| title_fullStr | An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients |
| title_full_unstemmed | An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients |
| title_short | An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients |
| title_sort | operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients |
| url | https://eprints.nottingham.ac.uk/2968/ https://eprints.nottingham.ac.uk/2968/ https://eprints.nottingham.ac.uk/2968/ |