Analysis of a two-phase field model for the solidification of an alloy

In this paper we present some theoretical results for a system of nonlinear partial differential equations that provide a phase field model for the solidification/melting of a metallic alloy. It is assumed that two different kinds of crystallization are possible. Consequently, the unknowns are the temperature tau and the phase field functions u and v. The time derivatives u(t) and v(t) appear in the equation for tau (the heat equation). On the other hand, the equations for u and v contain nonlinear terms where we find tau. (C) 2009 Elsevier Inc. All rights reserved.3571254