The Verigin problem with phase transitionLecture

by Dr Alice Marveggio

Thursday Nov 5, 2026, 9:30 AM → 10:15 AM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

We study the Verigin problem with phase transition, a free-boundary problem describing a compressible two-phase flow in a porous medium. We first present a variational approach based on the Wasserstein gradient-flow structure of the system. Through an implicit time discretization scheme, we construct distributional solutions satisfying an optimal energy-dissipation inequality. We then introduce a novel phase-field model, in which the sharp interface between the two phases is replaced by a thin transition layer of width $\varepsilon>0$. After establishing the existence of weak solutions, we prove convergence to a distributional solution of the Verigin problem with phase transition in the sharp-interface limit $\varepsilon\to0$.