Crystallization of polymeric materials is a phase-change process in strong
interaction with heat conduction. In typical example of moving boundary
problems such as Stefan problem, the unknown boundary is assumed to be
isothermal, which leads in a mathematical model to a homogeneous Dirichlet
condition for the (appropriate scaled) temperature. For polymers, the
situation is different, since the phase change does take place at a fixed
temperature (or with kinetic undercooling close to this temperature), but in
a rather large temperature range between the thermal melting point $T_m$ and
the glass transition temperature $T_g$. The local existence of smooth moving
front in was shown by Friedman- Velazquez under the assumption that initial
interface is small perturbation of a sphere. In this talk, we prove the
global existence of weak solution and show that temperature is Holder
continuous in space and the moving front is Lipschitz graph in time-space.