1.
Philos Trans A Math Phys Eng Sci
; 373(2050)2015 Sep 13.
Artículo
en Inglés
| MEDLINE
| ID: mdl-26261359
RESUMEN
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 (Hadzic & Shkoller 2014 Commun. Pure Appl. Math. 68, 689-757 (doi:10.1002/cpa.21522)) in which we studied nearly spherical shapes.