  We consider the flow of a viscous incompressible fluid through a porous
medium. We allow the permeability of the medium to depend exponentially on the
pressure and provide an analysis for this model. We study a splitting
formulation where a convection diffusion problem is used to define the
permeability, which is then used in a linear Darcy equation. We also study a
discretization of this problem, and provide an error analysis for it.
