| Abstract: |
| 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 analog 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. Finally, we propose a phase-field model for the Verigin problem with phase transition and study its sharp-interface limit. |
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