A Stefan problem with surface tension as the sharp interface limit of a nonlocal system of phase-field type

Reference:

Dirr, N., 2004. A Stefan problem with surface tension as the sharp interface limit of a nonlocal system of phase-field type. Journal of Statistical Physics, 114 (3-4), pp. 1085-1113.

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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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