Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media

Abstract

In this paper we consider the PDE describing the fluid flow in a porous medium, focusing on the solution’s dependence upon the choice of the saturation curve and the hydraulic conductivity. Basically, we consider two different saturation curves (say θ1 and θ2) and two different hydraulic conductivities (K1 and K2) which are both “close” in the L∞loc-norm. Then we find estimates to prove a constitutive stability for the solutions of the corresponding problems with the same boundary and initial conditions.