A phase-change model with a zone of coexistence of phases

A mathematical model for change of phase is presented, accounting for the presence of regions in which liquid and solid coexist. The basic variables are temperature θ and solid fraction v . We start from a relationship of the type θ = θ ( v ), supposed valid in thermodynamical equilibrium. Then for dynamical processes we introduce a perturbation causing v to be less than its equilibrium value in any solidification process. This solid fraction deficiency is governed by an ordinary differential equation containing θ t , in the forcing term. The heat-balance equation is in turn coupled to the ordinary differential equation through the term λ v t , (λ is latent heat). Some existence and uniqueness results are proved and some monotonicity properties are described for pure melting or pure solidification processes.