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Archive for Rational Mechanics and Analysis

, Volume 92, Issue 3, pp 205–245 | Cite as

An analysis of a phase field model of a free boundary

  • Gunduz Caginalp
Article

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.

Keywords

Neural Network Phase Transition Surface Tension Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag GmbH & Co. KG 1986

Authors and Affiliations

  • Gunduz Caginalp
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of PittsburghPittsburgh

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