Global stability of steady states in the classical Stefan problem
Published Web Locationhttps://arxiv.org/pdf/1501.00463.pdf
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result  in which we studied nearly spherical shapes.