On Gill's problem with anomalous diffusion

The classical formulation of Gill's theorem establishing the linear stability of the buoyant flow in a vertical porous channel subject to transverse diffusion and bounded by impermeable walls is here reconsidered from the perspective of anomalous mass diffusion. Anomalous diffusion is a physical effect implying a more general formulation of the governing equations of mass transfer either in a fluid or in a fluid-saturated porous medium. Anomalous diffusion is mathematically modelled via a diffusion equation with a time-dependent mass diffusivity. In this study, the stationary and parallel buoyant flow in a vertical porous layer saturated by a fluid is investigated. The implications of the anomalous diffusion model for the proof that such a flow is always linearly stable are analysed.