Speaker
Description
We consider a system of nonlinear partial differential equations that describes two-phase, two-component fluid flow in porous media. The system equations are obtained from the mass conservation law written for each component, to which initial and boundary conditions are added. For main unknows we select persistent variables, capable of modelling the flow in both the two-phase flow and the one-phase flow regions. We use an artificial persistent variable called global pressure and then rewrite this system in terms of global pressure and gas phase pseudo-pressure. As the obtained system contains degeneracy, we regularize it by a small parameter $\eta$. Furthermore, we apply time discretization, and introduce another persistent variable, called capillary pseudo-pressure. Since the global pressure partially decouples equations, we apply Schauder fixed point theorem easily and obtain the existence of solution at discrete time level. By passing to the limit in the time discretization parameter and afterwards in regularization parameter $\eta$, we prove the existence of weak solutions of the introduced initial-boundary value problem.
