Two-Phase Stefan Problem as the Limit Case of Two-Phase Stefan Problem with Kinetic Condition

Both one-dimensional two-phase Stefan problem with the thermodynamic equilibrium condition u(R(t),t)=0 and with the kinetic rule u (R (t),t)= R ′(t) at the moving boundary are considered. We prove, when approaches zero, R (t) converges to R(t) in C1+δ/2[0,T] for any finite T>0, 0<δ<1.