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
Noemi Wolanski, Julián Fernández Bonder, A free-boundary problem in combustion theory. Interfaces Free Bound. 2 (2000), no. 4, pp. 381–411