Electronic Resource
Springer
Continuum mechanics and thermodynamics
11 (1999), S. 173-179
ISSN:
1432-0959
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
A novel Liapunov functional was used in previous work to establish nonlinear stability of certain nontrivial equilibrium states; essentially the context was that of pure nonlinear diffusion. This paper uses the same Liapunov functional to derive a nonlinear stability criterion in the context of a highly nonlinear system of p.d.e.'s involving nonlinear diffusion as an element. The context is that of convection of a thermofluid (i) conforming to Darcy's law and the Boussinesq approximation, (ii) with temperature dependent thermal diffusivity and viscosity, in an infinite vertical slab of porous material. The vertical faces are held at different constant temperatures, a steady state is identified, and is shown to be nonlinearly stable provided that the Rayleigh number does not exceed a quantity which reflects the temperature dependence of the pertinent physical properties. It may be that the versatility of the Liapunov functional thus exhibited may extend to other nonlinear systems involving nonlinear diffusion.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s001610050109
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