Open AccessAn operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients
Author(s) -
Antony A. Hill,
M. S. Malashetty
Publication year - 2011
Publication title -
proceedings - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
eISSN - 1471-2946
pISSN - 1364-5021
DOI - 10.1098/rspa.2011.0137
Subject(s) - nonlinear system , instability , stability (learning theory) , monotonic function , convection , mathematics , mechanics , control theory (sociology) , statistical physics , physics , mathematical analysis , computer science , quantum mechanics , machine learning , control (management) , artificial intelligence
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