Two-phase Stefan problem as the limit case of two-phase Stefan problem with kinetic condition

Abstract

Both one-dimensional two-phase Stefan problem with the thermodynamic equilibrium condition u(R(t), t) = 0 and with the kinetic rule ue(Re(t), t) = eR'e(t) at the moving boundary are considered. We prove, when e approaches zero, Re(t) converges to R(t) in C1+δ/2[0, T] for any finite T > 0, 0 < δ < 1. © 2002 Elsevier Science (USA).