The Verigin problem with phase transition as Wasserstein flow

We study the modeling of a compressible two-phase flow in a porous medium. The governing PDE system is known as the Verigin problem with phase transition, which is the compressible analogue to the Muskat problem. We prove the convergence of an implicit time discretization scheme using the Wasserstein distance, obtaining distributional solutions in the limit that satisfy an optimal energy-dissipation rate. This talk is based on a joint work with Anna Kubin and Tim Laux.