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

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

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), https://doi.org/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: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 468
• Issue: 2138
• DOI: https://doi.org/10.1098/rspa.2011.0137
• Public URL: https://nottingham-repository.worktribe.com/output/709477
• Publisher URL: http://rspa.royalsocietypublishing.org/content/468/2138/323