Kinetic Undercooling Regularization of Supercooled Stefan Problems

In certain circumstances solutions of the one-phase supercooled Stefan problem in one space dimension with a constant melting temperature can blow up in finite time, with the free boundary moving with infinite speed. The inclusion of a kinetic term at the interface, so that the melting temperature is proportional to the speed, prevents this blow-up. The mathematical consequences of this regularization are discussed, and large-time asymptotic results described for solidification in a semi-infinite domain.