Well-posedness for a moving boundary model of an evaporation front in a porous medium

We consider a two-phase elliptic–parabolic moving boundary problem modelling an evaporation front in a porous medium. Our main result is a proof of short-time existence and uniqueness of strong solutions to the corresponding nonlinear evolution problem in an Lp-setting. It relies critically on nonstandard optimal regularity results for a linear elliptic–parabolic system with dynamic boundary condition.