JournalsifbVol. 15, No. 3pp. 281–322

Regularity of expanding front and its application to solidification/melting in undercooled liquid/superheated solid

  • Xinfu Chen

    University of Pittsburgh, United States
  • Huiqiang Jiang

    University of Pittsburgh, USA
Regularity of expanding front and its application to solidification/melting in undercooled liquid/superheated solid cover
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Abstract

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. 281–322

DOI 10.4171/IFB/304