On the solution of a generalized Stefan problem (Q1115165)

The authors considers a Stefan problem in which the interface velocity depends on the mean curvature of the interface. In the two-dimensional case they solve the equations numerically using Crank-Nicolson method, fourth-order differences and line relaxation. The numerical results confirm the stabilizing effect of surface curvature as predicted by \textit{J. Chadam} and \textit{P. Ortoleva} [IMA J. Appl. Math. 30, 57-66 (1983; Zbl 0544.35088)]. In the one-dimensional case the break-down time of the solution (infinite gradient on the interface) is estimated both theoretically (from above) and numerically.