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An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients

Hill, Antony A.; Malashetty, M.S.

Authors

Antony A. Hill antony.hill@nottingham.ac.uk

M.S. Malashetty



Abstract

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.

Citation

Hill, A. A., & Malashetty, M. (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), doi:10.1098/rspa.2011.0137

Journal Article Type Article
Publication Date Feb 8, 2012
Deposit Date Apr 16, 2014
Publicly Available Date Apr 16, 2014
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Electronic ISSN 1471-2946
Publisher Royal Society, The
Peer Reviewed Peer Reviewed
Volume 468
Issue 2138
DOI https://doi.org/10.1098/rspa.2011.0137
Public URL http://eprints.nottingham.ac.uk/id/eprint/2968
Publisher URL http://rspa.royalsocietypublishing.org/content/468/2138/323
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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