Onset of convection in a porous medium with internal heat source and variable gravity

The problem treated is that of convection in a fluid saturated porous layer, heated internally and where the gravitational field varies with distance through the layer. The boundaries are assumed to be solid. It is proved that the principle of exchange of stabilities holds as long as the gravity field and the integral of the heat sources both have the same sign. The proof is based on the idea of a positive operator, and uses th