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 ${\theta }_1$ and ${\theta }_2$) and two different hydraulic conductivities (${\mathcal{K}}_1$ and ${\mathcal{K}}_2$) which are both “close” in the $L_{\mathrm{loc}}^{\infty }$-norm. Then we find estimates to prove a constitutive stability for the solutions of the corresponding problems with the same boundary and initial conditions.