ON AN ASYMPTOTIC MODEL FOR FREE BOUNDARY DARCY FLOW IN POROUS MEDIA

2We provide a rigorous mathematical study of an asymptotic model describing Darcy flow with free boundary in a small amplitude/large wavelength approximation. In particular, we prove several well-posedness results in critical spaces. Furthermore, we also study how the solution decays towards the flat equilibrium.nonenoneGranero-Belinchon R; Scrobogna SGranero-Belinchon, R; Scrobogna,