Speaker
Description
We consider a phase-field model for multiphase flows in porous media coupling a Brinkman equation for the fluid motion with a generalized Cahn–Hilliard equation accounting for curvature-driven effects and mass exchange. We discuss existence results for the coupled system and, under suitable assumptions, uniqueness and continuous dependence properties. We further investigate the asymptotic transition to a Darcy-type model and establish existence of solutions for the limit problem. Finally, we address a distributed optimal control problem with the velocity field as control variable. We prove existence of optimal controls and derive first-order necessary optimality conditions by means of an adjoint system. The talk reports on a joint work with Gianni Gilardi (University of Pavia), Andrea Signori (Polytechnic of Milan), and Juergen Sprekels (WIAS Berlin and Humboldt University of Berlin).