Propagation profile for a non-Newtonian polytropic filtration equation with orientated convection

This paper is concerned with the propagation properties for a non-Newtonian polytropic filtration equation with orientated convection∂u∂t=div(|∇um|p−2∇um)−β→(x)⋅▿uq,x∈RN,t>0, where p>1p>1, m,q>0m,q>0, N≥1N≥1. Here, the orientation of the convection is specified to be either the convection with counteracting diffusion or the convection with promoting diffusion, that is β→(x)⋅(−x)≥0 or β→(x)⋅x≥0 respectively. By use of the super- and sub-solution method, we make complete classification of the three parameters m, p, q to characterize its propagation profile of solutions.