A stefan-like problem with a kinetic condition and surface tension effects

A two-dimensional, one phase Stefan-type problem is described as a model for an industrial erosion/deposition process, which includes surface tension effects and a kinetic condition at the free boundary. Special solutions (similarity and ‘traveling wave’) are considered. The stability of the free boundary of these special solutions is proved within the class of planar solutions, as is their linear stability as solutions of the full problem. The role of surface energy and the interaction rate in stabilizing solutions corresponding to deposition is discussed.