This paper presents a study of the relations between the modified Stefan problem in a plane and its quasi-steady approximation. In both cases the interfacial curve is assumed to be a polygon. It is shown that the weak solutions to the Stefan problem converge to weak solutions of the quasi-steady problem as the bulk specific heat tends to zero. The initial interface has to be convex of sufficiently small perimeter.
Cite this article
Piotr Rybka, On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling. Interfaces Free Bound. 2 (2000), no. 4, pp. 361–379DOI 10.4171/IFB/25