Abstract
A model for the evolution of phase boundaries reminiscent of the phase-field model is considered. The equation related to conservation of thermal energy is diffusive and coupled to an equation for the order parameter, which contains a nonlinear convolution operator, related to the limit of an interacting particle model with Kac-potential. Under diffusive rescaling the solutions converge to solutions of the Stefan problem with kinetic undercooling and surface tension.
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Dirr, N. A Stefan Problem with Surface Tension as the Sharp Interface Limit of a Nonlocal System of Phase-Field Type. Journal of Statistical Physics 114, 1085–1113 (2004). https://doi.org/10.1023/B:JOSS.0000012517.33719.9f
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DOI: https://doi.org/10.1023/B:JOSS.0000012517.33719.9f