Local existence of solutions of a three phase-field model for solidification

摘要

In this article we discuss the local existence and uniqueness of solutions of a system of parabolic differential partial equations modeling the process of solidification/melting of a certain kind of alloy. This model governs the evolution of the temperature field, as well as the evolution of three phase-field functions; the first two describe two different possible solid crystallization states and the last one describes the liquid state.