We consider a weakly coupled system, consisting of an elliptic equation and a degenerate parabolic equation; such a system arises in the theory of flow of immiscible fluids in a porous medium. The unknown functions u and v and the equations they satisfy, represent the pressure and the saturation respectively, subject to Darcy’s law and the Buckley-Leverett coupling. Due to the empirical nature of these laws no determination is possible on the structure of the degeneracy exhibited by the system. It is established that the saturation is a locally continuous function in its space-time domain of definition, irrespective of the nature of the degeneracy of the principal part of the system.
Continuity of the Saturation in the Flow of Two Immiscible Fluids in a Porous Medium
GIANAZZA, UGO PIETRO;
2010-01-01
Abstract
We consider a weakly coupled system, consisting of an elliptic equation and a degenerate parabolic equation; such a system arises in the theory of flow of immiscible fluids in a porous medium. The unknown functions u and v and the equations they satisfy, represent the pressure and the saturation respectively, subject to Darcy’s law and the Buckley-Leverett coupling. Due to the empirical nature of these laws no determination is possible on the structure of the degeneracy exhibited by the system. It is established that the saturation is a locally continuous function in its space-time domain of definition, irrespective of the nature of the degeneracy of the principal part of the system.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
