Non-linear stability bounds for a horizontal layer of a porous medium with an exothermic reaction on the lower boundary

We use the energy method to find regions of stability for a horizontal layer of a Darcy porous medium with an exothermic reaction on the lower layer. The results are compared to the linear instability results for this model found by Scott and Straughan [16]. It is shown that there is a region in which sub-critical instabilities may occur, but for small Lewis numbers, 0