On an Asymptotic Model for Free Boundary Darcy Flow in Porous Media
Rafael Granero-Belinchón, Stefano Scrobogna · SIAM Journal on Mathematical Analysis · 2020
We 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.