Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling (Q1193163)

The paper studies a modified Stefan problem which includes the ``modified Gibbs-Thomson relation'' on the free surface separating the solid and liquid phases. On the interface, the temperature \(u\) satisfies \(u=\sigma K-\beta V\), where \(K\) and \(V\) are the mean curvature and the normal velocity of the interface, respectively. Short term existence and uniqueness of classical solutions of the free boundary problem are obtained.