Global Weak Solutions to an Initial-Boundary Value Problem for a Three-phase Field Model of Solidification

Abstract

AbstractIn this article, we study an initial-boundary value problem for a three-phase field model of nonisothermal solidification processes in the case of two possible crystallization states. The governing equations of the model are the three phase-field equations coupled with a nonlinear heat equation. Each equation of the model has strong nonlinearities involving the higher-order derivatives. We prove the existence of global-in-time weak solutions to our problem for one-dimensional case.