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

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

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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.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1098/rspa.2011.0137
Depositing User: Johnson, Mrs Alison
Date Deposited: 16 Apr 2014 11:12
Last Modified: 13 Sep 2016 14:58
URI: http://eprints.nottingham.ac.uk/id/eprint/2968

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