  The classical one-phase Stefan problem describes the temperature distribution
in a homogeneous medium undergoing a phase transition, such as ice melting to
water. This is accomplished by solving the heat equation on a time-dependent
domain whose boundary is transported by the normal derivative of the
temperature along the evolving and a priori unknown free-boundary. We establish
a global-in-time stability result for nearly spherical geometries and small
temperatures, using a novel hybrid methodology, which combines energy
estimates, decay estimates, and Hopf-type inequalities.
