Two-phase Stefan problem with supercooling

Both one-dimensional two-phase Stefan problems with the thermodynamic equilibriumcondition θ(R(t),t)=0, and with the kinetic rule θ(R(t),t)=-ε̇R(t) at the moving boundary x=R(t) are considered. We study the properties of the regular solutions of the problem with equilibrium condition. They are obtained as a limit of solutions of the problem with the kinetic law as ε→0. The peculiarity of our problem is the partial supercooling of the liquid phase (θ<0) at the initial state.