This article proves that fronts of expanding domains with Hölder continuous speeds are contained in finite unions of Lipschitz graphs. As an application, the global in time existence of a solution to a free boundary problem modelling solidification in undercooled liquid or liquidation in superheated solid is established; here the propagation speed of the liquid/solid interface is assumed to be a known positive smooth function of the temperature, known as a kinetic undercooling/superheating effect.
Cite this article
Xinfu Chen, Huiqiang Jiang, Regularity of expanding front and its application to solidification/melting in undercooled liquid/superheated solid. Interfaces Free Bound. 15 (2013), no. 3, pp. 281–322DOI 10.4171/IFB/304