  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 $L_{p}$-setting. It relies critically on
nonstandard optimal regularity results for a linear elliptic-parabolic system
with dynamic boundary condition.
