Continuous Dependence on the Forchheimer Coefficient of the Forchheimer Fluid Interfacing with a Darcy Fluid

The continuous dependence of the two fluids which interface with each other in a bounded domain is derived. It is first shown how to establish the a priori results for the solutions for the flow in a bounded domain occupied by a viscous fluid in contact with a porous solid. It is also proved that the solution depends continuously on the Forchheimer coefficient