Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media
Mario Primicerio
Universita di Firenze, ItalyIacopo Borsi
TEASistemi SpA, Pisa, ItalyAngiolo Farina
Università di Firenze, ItalyRoberto Gianni
Università di Roma La Sapienza, Italy

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.
Cite this article
Mario Primicerio, Iacopo Borsi, Angiolo Farina, Roberto Gianni, Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 1, pp. 1–24
DOI 10.4171/RLM/531