Mathematical analysis of a degenerate porous-media equation for rock-dehydration processes

Abstract

In this paper, we establish the existence of weak solutions to quasilinear parabolic equations motivated by the geological modeling of rock-dehydration processes. These equations are charac- terized by a strongly degenerate Darcy coefficient, leading to a loss of ellipticity in the differential operator and to significant irregularities in the mass density. We propose a constructive approach based on a time–space discretization of a regularized problem, combined with uniform a priori estimates and compactness arguments to pass to the limit and recover a weak solution of the original system.