The stabilizing effect of surface tension on the development of the free boundary in a planar, one-dimensional, Cauchy-Stefan problem

A generalized Stefan problem which includes surface tension is presented as a mathematical model for the growth and melting of a solid. It is shown that planar melting is linearly morphologically stable with or without surface tension, while planar solidification is unstable without surface tension and is stabilized with its inclusion. The technique used is an adaptation to this situation of Rubinstein's recent work on the one-dimensional, two-phase problem without surface tension. 1