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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.

Journal Article Type Article
Publication Date Feb 8, 2012
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
Institution 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
DOI https://doi.org/10.1098/rspa.2011.0137
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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