Asymptotic results for the Stefan problem with kinetic undercooling

We study the behaviour of the one-phase Stefan problem with kinetic undercooling; moving boundary problems governed by the same formulation also arise in the modelling of silicon oxidation and of solvent diffusion in glassy polymers. The one-phase model is carefully derived from a two-phase formulation in the limit of small thermal diffusivity in the solid. A linear kinetic undercooling law is assumed at the moving boundary and the one-phase model is then studied in a number of asymptotic regimes. In particular, results for small and large Stefan number are presented in one dimension and in a paradigm two-dimensional example.