In this paper we present the phase-field models to describe
nonisothermal solidification of ideal multicomponent and multiphase
alloy systems. Governing equations are developed for the temporal and
spatial variation of three phase-field functions, as well as the
temperature field. The global existence of weak solutions to parabolic
differential equations in three dimension was proved by the Galerkin
method. The existence of a maximum theorem are also extensively studied.