Abstract
A mathematical analysis of a new approach to solidification problems is presented. A free boundary arising from a phase transition is assumed to have finite thickness. The physics leads to a system of nonlinear parabolic differential equations. Existence and regularity of solutions are proved. Invariant regions of the solution space lead to physical interpretations of the interface. A rigorous asymptotic analysis leads to the Gibbs-Thompson condition which relates the temperature at the interface to the surface tension and curvature.
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Communicated by C. M. Dafermos
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Caginalp, G. An analysis of a phase field model of a free boundary. Arch. Rational Mech. Anal. 92, 205–245 (1986). https://doi.org/10.1007/BF00254827
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DOI: https://doi.org/10.1007/BF00254827