Effect of anisotropic permeability on Darcy's law

The concept of structural stability is discussed and briefly reviewed withi n the context of fluid flow in porous media. Then the equations for non-Bou ssinesq (penetrative) convection in a porous medium with anisotropic permea bility are analysed. It is shown, by deriving truly a priori estimates, tha t the solution exists in the natural functional framework and depends conti nuously on changes in the permeability. Since under appropriate circumstanc es the onset of thermal convection may be via Hopf bifurcation rather than stationary convection, such a priori continuous dependence estimates are of much value. Copyright (C) 2001 John Wiley & Sons, Ltd.